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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 5 years ago

CBSE > Class 10 > Mathematics

1 answers

Tejasvini S 5 years 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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