CAT 2022 Slot 1 Paper

Question : 57 of 66

Marks: +1, -0

All the vertices of a rectangle lie on a circle of radius $\R$ . If the perimeter of the rectangle is $\P$ , then the area of the rectangle is

Solution:

\A=l b

l^2+b^2=4 r^2

P=2(l+b)

{\P}/{2}=l+b

Squaring on both the sides, we get

{\P^2}/{4}=l^2+b^2+2 l b

{\P^2}/{4}=4 r^2+2 l b

{\P^2}/{8}-2 r^2=l b

The answer is option B.

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