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Ask QuestionPosted by Aditya Singh 5 years, 2 months ago
- 2 answers
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Posted by Manika Sangal 5 years, 2 months ago
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Posted by R Divya Rajendran 5 years, 2 months ago
- 2 answers
Yogita Ingle 5 years, 2 months ago
5x-3y=3
x=0and y=k
5(0) - 3k = 3
0 - 3k = 3
k = 3/-3 = -1
Posted by Anshika Dubey 5 years, 2 months ago
- 1 answers
Romeo_ Gaming 5 years, 2 months ago
Posted by Abhishek Gautam 5 years, 2 months ago
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Posted by Sia Sharma 5 years, 2 months ago
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Gaurav Seth 5 years, 2 months ago
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = ½ AB
Solution:
(i) In ΔACB,
M is the midpoint of AB and MD || BC
, D is the midpoint of AC (Converse of mid point theorem)
(ii) ∠ACB = ∠ADM (Corresponding angles)
also, ∠ACB = 90°
, ∠ADM = 90° and MD ⊥ AC
(iii) In ΔAMD and ΔCMD,
AD = CD (D is the midpoint of side AC)
∠ADM = ∠CDM (Each 90°)
DM = DM (common)
, ΔAMD ≅ ΔCMD [SAS congruency]
AM = CM [CPCT]
also, AM = ½ AB (M is midpoint of AB)
Hence, CM = MA = ½ AB
Posted by Arun Kushwah 5 years, 2 months ago
- 1 answers
Yogita Ingle 5 years, 2 months ago
We have,
(99)3 =(100−1)3
We know that
(a−b)3=a3−b3−3ab(a−b)
Therefore,
=(100)3−13−3×100×1×(100−1)
=1000000−1−300(100−1)
=1000000−1−30000+300
=970299
Posted by Arun Kushwah 5 years, 2 months ago
- 2 answers
Posted by Arun Kushwah 5 years, 2 months ago
- 1 answers
Gaurav Seth 5 years, 2 months ago
Total number of families
= 475 + 814 + 211 = 1500
(i) Probability of a family, chosen at random,
having 2 girls = 
(ii) Probability of a family, chosen at random,
having 1 girl 
(iii) Probability of a family, chosen at random,
having no girl 
Sum of these probabilities
Hence, the sum is checked.
Posted by Arun Kushwah 5 years, 2 months ago
- 1 answers
Yogita Ingle 5 years, 2 months ago
Perimeter of isosceles triangle=30cm
Length of equal sides=12cm
Let third side of triangle=xcm
According to problem,
x+12+12=30
x+24=30
x=30−24
x=6
∴ Third side of triangle=6cm
Using Heron's formula
Area of triangle= √s(s−a)(s−b)(s−c) sq. units
where s= a+b+c/2
s= 30/2 =15
Area of triangle= √15(15−12)(15−12)(15−6) cm²
= √15×3×3×9 cm²
=3×3× √15cm²
=9√15cm²
∴ Area of triangle=9√15 cm
Posted by Arun Kushwah 5 years, 2 months ago
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Posted by Supriya Pattanayak 5 years, 2 months ago
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Punit Yadav 5 years, 2 months ago
Posted by Nidhi Shukla 5 years, 2 months ago
- 3 answers
Yogita Ingle 5 years, 2 months ago
If slant height is l and height is h and radius is r
As they form right angle triangle, By applying the Pythagorean Theorem,
then, the relation between them is represented as
l2 = h2 + r2
Punit Yadav 5 years, 2 months ago
Posted by Bom Tayeng 5 years, 2 months ago
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Posted by Kajal Kumari 5 years, 2 months ago
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Gaurav Seth 5 years, 2 months ago
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Posted by Sweta Yadav 5 years, 2 months ago
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Punit Yadav 5 years, 2 months ago
Posted by Aman Pal 5 years, 2 months ago
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Posted by Tanshu Sharma 5 years, 2 months ago
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Yogita Ingle 5 years, 2 months ago
If the opposite angles of a quadrilateral are equal, it is a parallelogram. The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, it is a parallelogram. If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.
Posted by Chetan Choudhary 5 years, 2 months ago
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Posted by Zainab Bano 5 years, 2 months ago
- 3 answers
Kajal Kumari 5 years, 2 months ago
Posted by Siddhant Gautam 5 years, 2 months ago
- 1 answers
Yogita Ingle 5 years, 2 months ago
Let ABCD be the parallelogram
Consider triangles ABC, BAD
AB=BA ... Common side
BC=AD ... Opp sides of llgm are equal
AC = BD ... Given
So triangles become cong by SSS rule.
Angle BAD = angle ABC ... CPCT
But sum of these angles is 180 as they are adjacent angles of llgm
So we can conclude that if each is equal to x
Therefore, 2x=180
Therefore, x=90
Thus ABCD is a parallelogram with one angle = 90 degrees
So, by the definition of parallelogram this is a rectangle.
Posted by Vansh Kakkar 5 years, 2 months ago
- 2 answers
Yogita Ingle 5 years, 2 months ago
Say an angle is 8x then the complement angle is x then we know two complementary angles sum up to 90∘.
So,
8x+x=90∘
9x=90∘
x=10∘
Hence, the angle is 80∘.
Posted by Aiswarya Raanee .K 5 years, 2 months ago
- 3 answers
Posted by Radheshyam Thakur 5 years, 3 months ago
- 1 answers
Yogita Ingle 5 years, 3 months ago
Drop a perpendicular from O to both chords AB and CD
In △OMP and △ONP
As chords are equal, perpendicular from centre would also be equal.
OM=ON
OP is common.
∠OMP=∠ONP=90o
△OMP ≅ △ONP (RHS Congruence)
PM=PN ......................(1)
AM=BM (Perpendicular from centre bisects the chord)
Similarly ,CN=DN
As AB=CD
AB−AM=CD−DN
BM=CN .........................(2)
From (1) and (2)
BM−PM=CN−PN
PB=PC
AM=DN (Half the length of equal chords are equal)
AM+PM=DN+PN
AP=PD
Therefore , PB=PC and AP=PD is proved.
Posted by Gyan Prakash 5 years, 3 months ago
- 1 answers
Ayush Kumar 5 years, 3 months ago
Posted by Reshma . B 5 years, 3 months ago
- 1 answers
Ayush Kumar 5 years, 3 months ago
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Harshit Kohli 5 years, 2 months ago
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