cat 2022 Question 11

Question

A trapezium ABCD has side AD parallel to $ ext{BC}, \angle ext{BAD}=90^{\circ}, ext{BC}=3 ext{~cm}$ and AD=8~cm . If the perimeter of this trapezium is 36~cm, then its area, in sq.cm, is

Accepted Answer

CD = $\sqrt{y^2 + 25}$

$11 + y + \sqrt{y^2 + 25} = 36$

$\sqrt{y^2 + 25} = 25 - y$

$y^2 + 25 = 25^2 + y^2 - 50y$

$2y = 24$

y = 12

Question 11.

Question Explanation