Question 57
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
$$A=lb$$
$$l^2+b^2=4r^2$$
$$P\ =2\left(l+b\right)$$
$$\frac{P}{2}=l+b$$
Squaring on both the sides, we get
$$\frac{P^2}{4}=l^2+b^2+2lb$$
$$\frac{P^2}{4}=4r^2+2lb$$
$$\frac{P^2}{8}-2r^2=lb$$
The answer is option B.
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