CAT 2022 Slot 1 QA Question 18: 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

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

Let the sides of the rectangle be $l$ and $b$. Since all vertices lie on a circle of radius $R$, the diagonal of the rectangle is the diameter of the circle.
$l^2 + b^2 = (2R)^2 = 4R^2$
$P = 2(l+b)$
$l+b = \dfrac{P}{2}$
Now square the sum of the sides.
$(l+b)^2 = l^2 + b^2 + 2lb$
$\Rightarrow \dfrac

All the vertices of a rectangle lie on a circle of radius RRR. If the perimeter of the rectangle is PPP, then the area of the rectangle is

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