{"id":4968,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-5\/"},"modified":"2018-06-08T14:46:31","modified_gmt":"2018-06-08T09:16:31","slug":"ncert-solutions-for-class-10-maths-exercise-6-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 6.5"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#NCERT_Solutions_for_Class_10_Maths_Triangles\" >NCERT Solutions for Class 10 Maths\u00a0Triangles<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#1_Sides_of_triangles_are_given_below_Determine_which_of_them_are_right_triangles_In_case_of_a_right_triangle_write_the_length_of_its_hypotenuse\" >1. Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#3_In_figure_ABD_is_a_triangle_right_angled_at_A_and_ACBD_Show_that\" >3. In figure, ABD is a triangle right angled at A and ACBD. Show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#4_ABC_is_an_isosceles_triangle_right_angled_at_C_Prove_that\" >4. ABC is an isosceles triangle right angled at C. Prove that.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#5_ABC_is_an_isosceles_triangle_with_AC_BC_If_prove_that_ABC_is_a_right_triangle\" >5. ABC is an isosceles triangle with AC = BC. If, prove that ABC is a right triangle.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#6_ABC_is_an_equilateral_triangle_of_side_Find_each_of_its_altitudes\" >6. ABC is an equilateral triangle of side  Find each of its altitudes.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#7_Prove_that_the_sum_of_the_squares_of_the_sides_of_a_rhombus_is_equal_to_the_sum_of_squares_of_its_diagonals\" >7. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of squares of its diagonals.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#8_In_figure_O_is_a_point_in_the_interior_of_a_triangle_ABC_OD_BC\" >8. In figure, O is a point in the interior of a triangle ABC, OD BC,<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#9_A_ladder_10_m_long_reaches_a_window_8_m_above_the_ground_Find_the_distance_of_the_foot_of_the_ladder_from_base_of_the_wall\" >9. A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#10_A_guy_wire_attached_to_a_vertical_pole_of_height_18_m_is_24_m_long_and_has_a_stake_attached_to_the_other_hand_How_far_from_the_base_of_the_pole_should_the_stake_be_driven_so_that_the_wire_will_be_taut\" >10. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other hand. How far from the base of the pole should the stake be driven so that the wire will be taut?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#11_An_aeroplane_leaves_an_airport_and_flies_due_north_at_a_speed_of_1000_km_pwe_hour_At_the_same_time_another_aeroplane_leaves_the_same_airport_and_flies_due_west_at_a_speed_of_1200_km_per_hour_How_far_apart_will_be_the_two_planes_after_hours\" >11. An aeroplane leaves an airport and flies due north at a speed of 1000 km pwe hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after  hours?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#12_Two_poles_of_heights_6_m_and_11_m_stand_on_a_plane_ground_If_the_distance_between_the_feet_of_the_poles_is_12_m_find_the_distance_between_their_tops\" >12. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#13_D_and_E_are_points_on_the_sides_CA_and_CB_respectively_of_a_triangle_ABC_right_angled_at_C_Prove_that\" >13. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that =.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#14_The_perpendicular_from_A_on_side_BC_of_a_ABC_intersects_BC_at_D_such_that_DB_3CD_see_figure_Prove_that\" >14. The perpendicular from A on side BC of a ABC intersects BC at D such that DB = 3CD (see figure). Prove that.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#15_In_an_equilateral_triangle_ABC_D_is_a_point_on_side_BC_such_that_BD_BC_Prove_that\" >15. In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#16_In_an_equilateral_triangle_prove_that_three_times_the_square_of_one_side_is_equal_to_four_times_the_square_of_one_of_its_altitudes\" >16. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#17_Tick_the_correct_answer_and_justify_In_ABC_AB_cm_AC_12_cm_and_BC_6_cm_the_angles_A_and_B_are_respectively\" >17. Tick the correct answer and justify: In ABC, AB =  cm, AC = 12 cm and BC = 6 cm. the angles A and B are respectively:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#NCERT_Solutions_for_Class_10_Maths_Exercise_65\" >NCERT Solutions for Class 10 Maths Exercise 6.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 6.5 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Maths Triangles<\/strong><strong>\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics-triangles\/1208\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/10%20Maths%20Book.jpg\" alt=\"NCERT Solutions for Class 10 Maths Exercise 6.5\" width=\"163\" height=\"201\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Triangles\"><\/span>NCERT Solutions for Class 10 Maths\u00a0Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Sides_of_triangles_are_given_below_Determine_which_of_them_are_right_triangles_In_case_of_a_right_triangle_write_the_length_of_its_hypotenuse\"><\/span><strong>1. Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i)7 cm, 24 cm, 25 cm <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) 3 cm, 8 cm, 6 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)50 cm, 80 cm, 100 cm <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)13 cm, 12 cm, 5 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Let <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image001.png\" \/>= 7 cm, <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image002.png\" \/>= 24 cm and <img decoding=\"async\" style=\"height: 15px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image003.png\" \/>= 25 cm<\/p>\n<p style=\"text-align: justify;\">Here the larger side is <img decoding=\"async\" style=\"height: 15px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image003.png\" \/>= 25 cm.<\/p>\n<p style=\"text-align: justify;\">We have, <img decoding=\"async\" style=\"height: 21px; width: 254px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">So, the triangle with the given sides is a right triangle. Its hypotenuse = 25 cm<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Let <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image001.png\" \/>= 3 cm, <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image002.png\" \/>= 8 cm and <img decoding=\"async\" style=\"height: 15px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image003.png\" \/>= 6 cm<\/p>\n<p style=\"text-align: justify;\">Here the larger side is <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image002.png\" \/>= 8 cm.<\/p>\n<p style=\"text-align: justify;\">We have, <img decoding=\"async\" style=\"height: 21px; width: 221px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\">So, the triangle with the given sides is not a right triangle.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Let <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image001.png\" \/>= 50 cm, <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image002.png\" \/>= 80 cm and <img decoding=\"async\" style=\"height: 15px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image003.png\" \/>= 100 cm<\/p>\n<p style=\"text-align: justify;\">Here the larger side is<img decoding=\"async\" style=\"height: 15px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image003.png\" \/>= 100 cm.<\/p>\n<p style=\"text-align: justify;\">We have, <img decoding=\"async\" style=\"height: 21px; width: 293px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">So, the triangle with the given sides is not a right triangle.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> Let <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image001.png\" \/>= 13 cm, <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image002.png\" \/>= 12 cm and <img decoding=\"async\" style=\"height: 15px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image003.png\" \/>= 5 cm<\/p>\n<p style=\"text-align: justify;\">Here the larger side is <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image001.png\" \/>= 13 cm.<\/p>\n<p style=\"text-align: justify;\">We have, <img decoding=\"async\" style=\"height: 21px; width: 249px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">So, the triangle with the given sides is a right triangle. Its hypotenuse = 13 cm<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<p><strong>2. PQR is a triangle right angled at P and M is a point on QR such that PM\u00a0<img decoding=\"async\" title=\"Double click to edit\" src=\"http:\/\/cdn.topperlearning.com\/topper\/bookquestions\/323_cd0ab85520b5ae722383bdcc2bb17bd8.png\" alt=\"\" align=\"middle\" data-pin-nopin=\"true\" data-cke-saved-src=\"http:\/\/cdn.topperlearning.com\/topper\/bookquestions\/323_cd0ab85520b5ae722383bdcc2bb17bd8.png\" \/>\u00a0QR. Show that PM<sup>2<\/sup>\u00a0= QM x MR. <\/strong><\/p>\n<p><strong>Ans. Given<\/strong>: PQR is a triangle right angles at P and PM<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>QR<\/p>\n<p><img decoding=\"async\" id=\"Picture 27\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image009.jpg\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image009.jpg\" \/><\/p>\n<p><strong>To Prove<\/strong>: PM<sup>2<\/sup> = QM.MR<\/p>\n<p><strong>Proof<\/strong>: Since PM<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>QR<br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>QMP<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image012.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image012.png\" \/>PMR<br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"0\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7BQM%7D%7BPM%7D%20%3D%20%5C%5Cfrac%7BPM%7D%7BRM%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{QM}{PM} = \\frac{PM}{RM}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image015.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image015.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_In_figure_ABD_is_a_triangle_right_angled_at_A_and_ACBD_Show_that\"><\/span><strong>3. In figure, ABD is a triangle right angled at A and AC<\/strong><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/><strong>BD. Show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) AB<sup>2<\/sup> = BC.BD<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) AC<sup>2<\/sup> = BC.DC<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) AD<sup>2<\/sup> = BD.CD<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1\" style=\"height: 143px; width: 122px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image016.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: ABD is a triangle right angled at A and AC<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>BD.<\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: <strong>(i)<\/strong> AB<sup>2<\/sup> = BC.BD, <strong>(ii) <\/strong><img decoding=\"async\" style=\"height: 24px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image017.png\" \/><strong>(iii) <\/strong><img decoding=\"async\" style=\"height: 22px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>:<strong>(i)<\/strong> Since AC<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>BD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC<img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image012.png\" \/>ADC and each triangle is similar to <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC<img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image012.png\" \/>ABD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 28\" style=\"height: 121px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image019.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong>Since <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC<img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image012.png\" \/>ADC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Since <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ACD<img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image012.png\" \/>ABD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image018.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_ABC_is_an_isosceles_triangle_right_angled_at_C_Prove_that\"><\/span><strong>4. ABC is an isosceles triangle right angled at C. Prove that<img decoding=\"async\" style=\"height: 22px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image025.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since ABC is an isosceles right triangle, right angled at C.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image027.png\" \/>[BC = AC, given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image028.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_ABC_is_an_isosceles_triangle_with_AC_BC_If_prove_that_ABC_is_a_right_triangle\"><\/span><strong>5. ABC is an isosceles triangle with AC = BC. If<img decoding=\"async\" style=\"height: 22px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image028.png\" \/>, prove that ABC is a right triangle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since ABC is an isosceles right triangle with AC = BC and <img decoding=\"async\" style=\"height: 22px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image026.png\" \/> [BC = AC, given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC is right angled at C.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_ABC_is_an_equilateral_triangle_of_side_Find_each_of_its_altitudes\"><\/span><strong>6. ABC is an equilateral triangle of side <\/strong><img decoding=\"async\" style=\"height: 19px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image029.png\" \/><strong> Find each of its altitudes.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let ABC be an equilateral triangle of side <img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image030.png\" \/> units.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 29\" style=\"height: 137px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image031.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Draw AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>BC. Then, D is the mid-point of BC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> BD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image032.png\" \/>BC = <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since, ABD is a right triangle, right triangle at D.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 29px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image035.png\" \/>= AD<sup>2<\/sup> + <img decoding=\"async\" style=\"height: 29px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image037.png\" \/>= <img decoding=\"async\" style=\"height: 21px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> Each of its altitude = <img decoding=\"async\" style=\"height: 24px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image039.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Prove_that_the_sum_of_the_squares_of_the_sides_of_a_rhombus_is_equal_to_the_sum_of_squares_of_its_diagonals\"><\/span><strong>7. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of squares of its diagonals.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the diagonals AC and BD of rhombus ABCD intersect each other at O. Since the diagonals of a rhombus bisect each other at right angles.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image040.png\" \/><img decoding=\"async\" style=\"height: 21px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image041.png\" \/> and AO = CO, BO = OD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 30\" style=\"height: 90px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since AOB is a right triangle, right angled at O.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image044.png\" \/>= <img decoding=\"async\" style=\"height: 49px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\">[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image046.png\" \/>OA = OC and OB = OD]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image047.png\" \/>\u2026\u2026\u2026.(1)<\/p>\n<p style=\"text-align: justify;\">Similarly, we have <img decoding=\"async\" style=\"height: 22px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image048.png\" \/>\u2026\u2026\u2026.(2)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image049.png\" \/>\u2026\u2026\u2026.(3)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 138px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image050.png\" \/>\u2026\u2026\u2026.(4)<\/p>\n<p style=\"text-align: justify;\">Adding all these results, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 29px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image051.png\" \/>= <img decoding=\"async\" style=\"height: 29px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image053.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image054.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_In_figure_O_is_a_point_in_the_interior_of_a_triangle_ABC_OD_BC\"><\/span><strong>8. In figure, O is a point in the interior of a triangle ABC, OD<\/strong><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/><strong> BC, <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>OE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/> AC and OF<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/> AB. Show that:<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 15\" style=\"height: 160px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image055.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 22px; width: 254px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image056.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image057.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image057.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image058.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Join AO, BO and CO.<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> In right <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>s OFA, ODB and OEC, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image059.png\" \/>,<img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image060.png\" \/> and<img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 32\" style=\"height: 138px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image062.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Adding all these, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image063.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 248px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image064.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 246px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image065.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image066.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> In right <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>s ODB and ODC, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image060.png\" \/> and <img decoding=\"async\" style=\"height: 22px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image067.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image068.png\" \/>\u2026\u2026\u2026.(1)<\/p>\n<p style=\"text-align: justify;\">Similarly, we have <img decoding=\"async\" style=\"height: 22px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image068.png\" \/>\u2026\u2026\u2026.(2)<\/p>\n<p style=\"text-align: justify;\">and<img decoding=\"async\" style=\"height: 22px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image069.png\" \/> = <img decoding=\"async\" style=\"height: 22px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image070.png\" \/>\u2026\u2026\u2026.(3)<\/p>\n<p style=\"text-align: justify;\">Adding equations (1), (2) and (3), we get<\/p>\n<p style=\"text-align: justify;\">=<img decoding=\"async\" style=\"height: 29px; width: 287px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image071.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 285px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image072.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/><img decoding=\"async\" style=\"height: 29px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image073.png\" \/>\u2013<img decoding=\"async\" style=\"height: 29px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image074.png\" \/>= 0<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image066.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image075.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_A_ladder_10_m_long_reaches_a_window_8_m_above_the_ground_Find_the_distance_of_the_foot_of_the_ladder_from_base_of_the_wall\"><\/span><strong>9. A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let AB be the ladder, B be the window and CB be the wall. Then, ABC is a<\/p>\n<p style=\"text-align: justify;\">right triangle, right angled at C.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 33\" style=\"height: 112px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image076.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image078.png\" \/>= 100 \u2013 64<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image078.png\" \/>= 36<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> AC = 6<\/p>\n<p style=\"text-align: justify;\">Hence, the foot of the ladder is at a distance 6 m from the base of the wall.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_A_guy_wire_attached_to_a_vertical_pole_of_height_18_m_is_24_m_long_and_has_a_stake_attached_to_the_other_hand_How_far_from_the_base_of_the_pole_should_the_stake_be_driven_so_that_the_wire_will_be_taut\"><\/span><strong>10. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other hand. How far from the base of the pole should the stake be driven so that the wire will be taut?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let AB (= 24m) be a guy wire attached to a vertical pole. BC of height 18 m. To keep the wire taut, let it be fixed to a stake at A. Then, ABC is a right triangle, right angled at C.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 35\" style=\"height: 107px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image079.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image078.png\" \/>= 576 \u2013 324<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image078.png\" \/>= 252<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> AC = 6<img decoding=\"async\" style=\"height: 24px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image081.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence, the stake may be placed at distance of 6<img decoding=\"async\" style=\"height: 24px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image081.png\" \/>m from the base of the pole.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_An_aeroplane_leaves_an_airport_and_flies_due_north_at_a_speed_of_1000_km_pwe_hour_At_the_same_time_another_aeroplane_leaves_the_same_airport_and_flies_due_west_at_a_speed_of_1200_km_per_hour_How_far_apart_will_be_the_two_planes_after_hours\"><\/span><strong>11. An aeroplane leaves an airport and flies due north at a speed of 1000 km pwe hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after <\/strong><img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image082.png\" \/><strong> hours?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the first aeroplane starts from O and goes upto A towards north where<\/p>\n<p style=\"text-align: justify;\">OA = <img decoding=\"async\" style=\"height: 45px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image083.png\" \/>km = 1500 km<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 65\" style=\"height: 192px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image084.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let the second aeroplane starts from O at the same time and goes upto 1500 km<\/p>\n<p style=\"text-align: justify;\">B towards west where<\/p>\n<p style=\"text-align: justify;\">OB = <img decoding=\"async\" style=\"height: 45px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image085.png\" \/>km = 1800 km<\/p>\n<p style=\"text-align: justify;\">According to the question the required distance = BA<\/p>\n<p style=\"text-align: justify;\">In right angled triangle ABC, by Pythagoras theorem, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 122px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image086.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 2250000 + 3240000<\/p>\n<p style=\"text-align: justify;\">= 5490000 = <img decoding=\"async\" style=\"height: 19px; width: 110px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image087.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> AB = <img decoding=\"async\" style=\"height: 24px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image088.png\" \/>km<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Two_poles_of_heights_6_m_and_11_m_stand_on_a_plane_ground_If_the_distance_between_the_feet_of_the_poles_is_12_m_find_the_distance_between_their_tops\"><\/span><strong>12. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let AB = 11 m and CD = 6 m be the two poles such that BD = 12 m A<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 36\" style=\"height: 123px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image089.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Draw CE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>AB and join AC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> CE = DB = 12 m<\/p>\n<p style=\"text-align: justify;\">AE = AB \u2013 BE = AB \u2013 CD = (11 \u2013 6)m = 5 m<\/p>\n<p style=\"text-align: justify;\">In right angled triangle ACE, by Pythagoras theorem, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image090.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image091.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 144 + 25 = 169<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> AC = 13 m<\/p>\n<p style=\"text-align: justify;\">Hence, the distance between the tops of the two poles is 13 m.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_D_and_E_are_points_on_the_sides_CA_and_CB_respectively_of_a_triangle_ABC_right_angled_at_C_Prove_that\"><\/span><strong>13. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that <img decoding=\"async\" style=\"height: 20px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image092.png\" \/>=<img decoding=\"async\" style=\"height: 20px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image093.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>In right angled <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>s ACE and DCB, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 38\" style=\"height: 134px; width: 110px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image094.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image095.png\" \/>and <img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image097.png\" \/>= <img decoding=\"async\" style=\"height: 29px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image098.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image097.png\" \/>= <img decoding=\"async\" style=\"height: 29px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image099.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image097.png\" \/>= <img decoding=\"async\" style=\"height: 20px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image100.png\" \/><\/p>\n<p style=\"text-align: justify;\">[By Pythagoras theorem, <img decoding=\"async\" style=\"height: 22px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image101.png\" \/> and <img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image102.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_The_perpendicular_from_A_on_side_BC_of_a_ABC_intersects_BC_at_D_such_that_DB_3CD_see_figure_Prove_that\"><\/span><strong>14. The perpendicular from A on side BC of a <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/><strong>ABC intersects BC at D such that DB = 3CD (see figure). Prove that<img decoding=\"async\" style=\"height: 22px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image103.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 26\" style=\"height: 140px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image104.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We have, DB = 3CD<\/p>\n<p style=\"text-align: justify;\">Now, BC = DB + CD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> BC = 3CD + CD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> BC = 4CD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> CD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image105.png\" \/>BC and DB = 3CD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image106.png\" \/>BC \u2026\u2026\u2026.(1)<\/p>\n<p style=\"text-align: justify;\">Since, \u2206 ABD is a right triangle, right angled at D. Therefore by Pythagoras theorem, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 20px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image107.png\" \/>\u2026\u2026\u2026.(2)<\/p>\n<p style=\"text-align: justify;\">Similarly, from <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ACD, we have, <img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image108.png\" \/>\u2026\u2026\u2026.(3)<\/p>\n<p style=\"text-align: justify;\">From eq. (2) and (3)<img decoding=\"async\" style=\"height: 22px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image109.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image110.png\" \/>= <img decoding=\"async\" style=\"height: 49px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image111.png\" \/> [Using eq.(1)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image110.png\" \/>= <img decoding=\"async\" style=\"height: 45px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image112.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> AB<sup>2<\/sup> \u2013 AC<sup>2<\/sup> = <img decoding=\"async\" style=\"height: 41px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image113.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image114.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image115.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_In_an_equilateral_triangle_ABC_D_is_a_point_on_side_BC_such_that_BD_BC_Prove_that\"><\/span><strong>15. In an equilateral triangle ABC, D is a point on side BC such that BD = <\/strong><img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image116.png\" \/><strong>BC. Prove that<img decoding=\"async\" style=\"height: 22px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image117.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let ABC be an equilateral triangle and let D be a point on BC such that BD = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image116.png\" \/>BC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 132px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image118.png\" \/><\/p>\n<p style=\"text-align: justify;\">Draw AE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>BC, Join AD.<\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>s AEB and AEC, we have,<\/p>\n<p style=\"text-align: justify;\">AB = AC[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image046.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC is equilateral]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>AEB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>AEC [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image046.png\" \/> each <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/>]\n<p style=\"text-align: justify;\">And AE = AE<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> By SAS-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>AEB <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image121.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>AEC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> BE = EC<\/p>\n<p style=\"text-align: justify;\">Thus, we have, BD = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image116.png\" \/>BC, DC = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image122.png\" \/>BC and BE = EC = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image116.png\" \/>BC \u2026\u2026\u2026(1)<\/p>\n<p style=\"text-align: justify;\">Since, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image123.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ADC is an acute angle triangle.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 206px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image124.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 224px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image125.png\" \/>[using eq.(1)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image126.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image127.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image046.png\" \/> AB = BC = AC]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 20px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image037.png\" \/>=<img decoding=\"async\" style=\"height: 45px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image128.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image129.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_In_an_equilateral_triangle_prove_that_three_times_the_square_of_one_side_is_equal_to_four_times_the_square_of_one_of_its_altitudes\"><\/span><strong>16. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let ABC be an equilateral triangle and let AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image008.png\" \/>BC. In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>s ADB and ADC, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 40\" style=\"height: 126px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image130.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">AB = AC [Given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image123.png\" \/>[Given]\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>ADB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>ADC[Each = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/>]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ADB <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image131.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ADC[By RHS criterion of congruence]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> BD = DC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> BD = DC = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image032.png\" \/>BC<\/p>\n<p style=\"text-align: justify;\">Since <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ADB is a right triangle, right angled at D, by Pythagoras theorem, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 20px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 150px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image132.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image133.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image134.png\" \/>[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image046.png\" \/> BC = AB]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image135.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image136.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"17_Tick_the_correct_answer_and_justify_In_ABC_AB_cm_AC_12_cm_and_BC_6_cm_the_angles_A_and_B_are_respectively\"><\/span><strong>17. Tick the correct answer and justify: In <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/><strong>ABC, AB = <\/strong><img decoding=\"async\" style=\"height: 24px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image137.png\" \/><strong> cm, AC = 12 cm and BC = 6 cm. the angles A and B are respectively:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/> and <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image138.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/> and <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image123.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image138.png\" \/> and <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image123.png\" \/> and <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (C)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC, we have, AB = <img decoding=\"async\" style=\"height: 24px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image137.png\" \/>cm, AC = 12 cm and BC = 6 cm.<\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 22px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image139.png\" \/>= <img decoding=\"async\" style=\"height: 36px; width: 240px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image140.png\" \/>= 144 = <img decoding=\"async\" style=\"height: 29px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image141.png\" \/><\/p>\n<p style=\"text-align: justify;\">Thus, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>ABC is a right triangle, right angled at B.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>B = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 41\" style=\"height: 132px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image142.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Let D be the mid-point of AC. We know that the mid-point of the hypotenuse of a right triangle is equidistant from the vertices.<\/p>\n<p style=\"text-align: justify;\">AD = BD = CD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> CD = BD = 6 cm [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image046.png\" \/> CD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image032.png\" \/>AC]\n<p style=\"text-align: justify;\">Also, BC = 6 cm<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>BDC, we have, BD = CD = BC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image011.png\" \/>BDC is equilateral<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image013.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>ACB = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image123.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>A = <img decoding=\"async\" style=\"height: 29px; width: 284px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image143.png\" \/><\/p>\n<p style=\"text-align: justify;\">Thus, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>A = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image138.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image119.png\" \/>B = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.5\/image120.png\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_65\"><\/span>NCERT Solutions for Class 10 Maths Exercise 6.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE\u00a0<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 6.5 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class &#8230; <a title=\"NCERT Solutions for Class 10 Maths Exercise 6.5\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-5\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Exercise 6.5\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1347,281],"tags":[283,438,321,1485,216],"class_list":["post-4968","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-ncert-solutions","tag-cbse-study-material","tag-class-10","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Exercise 6.5 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Exercise 6.5 in PDF format for free download. 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