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In triangle ABC, AB = AC = 25 and BC = \(20\). Points D, E and F are on sides AB, BC and AC respectively, such that DE and EF are parallel to AC  and AB respectively. What is the perimeter of parallelogram ADEF?

 

 

 Jan 18, 2022
 #1
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Since triangleEFC is iscoceles, AF+FC=AF+FE=25. This is also true for DE with triangleBDE also being iscoceles and AD+DB=AD+DE=25.

The perimeter of the paralellogram is (AD+DE)+(AF+FE) and we know that AD+DE=25 and AF+FE=25, so the answer is 25+25=50.

 

Hope this helped.

 Jan 18, 2022

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