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ABC is an isosceles triangle right …

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ABC is an isosceles triangle right angled at B. Two equilateral triangles are constructed with side BC and AC show that area of triangle BCD=1/2area of triangle ACE.

Posted by Harshit Bhandekar 4 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Tejasvini S 4 years, 10 months ago

Given that:- △ABC is an isosceles triangle and ∠ABC=90° ∴AB=BC △ABE∼△ACD(∵All equilateral triangles are similar) To find:- ar(△ACD) ar(△ABE) =? Solution:- In △ABC, Using pythagoras theorem, AC 2 =AB 2 +BC 2 AC 2 =AB 2 +AB 2 [∵AB=AC] AC 2 =2AB 2 .....(i) Now In △ABE and △ACD △ABE∼△ACD(Given), As we know that ratio of area of similar triangles is equal to the ratio of squares of their corresponding sides. ∴ ar(△ACD) ar(△ABE) = AC 2 AB 2 ⇒ ar(△ACD) ar(△ABE) = 2AB 2 AB 2 [From(i)] ⇒ ar(△ACD) ar(△ABE) = 2 1 ⇒ar(△ABE):ar(△ACD)=1:2 Hence the ratio between the area of △ABE to the area of △ACD is 1:2.

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

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Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
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