A rectangle of length ‘x’ and breadth ‘y’ is inscribed in a semi-circle of fixed radius ‘r’ as shown in the figure given below. Based on the above information answer the following question:

The value of θ, for which A'(θ) = 0 is

π \(\frac{π}{2}\) \(\frac{π}{4}\) \(\frac{π}{3}\)

\(\frac{π}{4}\)

$A'(θ)=0$ $A=r^2sin2θ$ $A'=2r^2cos2θ=0$ $2θ=(2n+1)\frac{\pi}{2}$ $θ =(2n+1)\frac{\pi}{4}⇒θ = \frac{\pi}{4}$ Option C is correct.