CAT 2025 Slot 3 QA Question 32: 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

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

In rectangle ABCD, $CD = AB = 56$ cm. Since E is the midpoint of CD, $DE = 28$ cm.
Triangle ADE is right-angled at D, with $AD = 45$ cm and $DE = 28$ cm.
$AE = \sqrt{45^2 + 28^2}$
$= \sqrt{2025 + 784}$
$= \sqrt{2809}$
$= 53$
For a right triangle, the inradius is $\dfrac{	ext{sum of legs} - 	ext{hy

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 △ADE\triangle ADE△ADE is

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 $\triangle ADE$ is