Rectangles are inscribed inside a semi-circle of radius `rdot` Find the rectangle with maximum area.

Explanation

Let us choose coordinate system with the origin as the center of circel.

Area of rectangle PQRS
A=2(r cos `theta`)(r sin `theta`), `theta` in `(0,(pi)/(2))`
A=`r^(2) sin 2 theta`
A is maximum when sin 2 `theta` =1 or 2 `theta =pi//2`
`theta =pi//4`
Therefore sides of the rectangle are 2r cos`(pi//4)=sqrt(2r)`and r sin `(pi//4)=rsqrt(2)`