cat 2024 Question 19

Question

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of $ riangle ADE$ is

Accepted Answer

Drawing the figure described in the question, we get the following representation,

Since E is the midpoint of CD, the length of each half will be 28cm.

We need to find the incircle of the triangle ADE, which is a right angled triangle, we can do that with the formula,

$\dfrac{\left(a+b-h\right)}{2}$

$h^2=28^2+45^2$

$h^2=784+2025=2809$

$h=53$

$r=\dfrac{\left(28+45-53\right)}{2}=10$

Question 19.

Question Explanation