cat 2022 Question 19

Question

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

Accepted Answer

$A = lb$

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

$P = 2(l + b)$

$\frac{P}{2} = l + b$

Squaring on both the sides, we get

$\frac{P^2}{4} = l^2 + b^2 + 2lb$

$\frac{P^2}{4} = 4r^2 + 2lb$

$\frac{P^2}{8} - 2r^2 = lb$

Question 19.