2025 AHS PRELIMS P2 Q8

In the figure, \(PQRS\) is a rectangle which fits inside a semicircle of radius 8 cm and centre \(O\).

If \(PQ=x\) cm and \(QR=y\) cm,

1. Show that the area of the rectangle, \(A\text{ cm}^2\), is given by \(A=\dfrac{x}{2}\sqrt{256-x^2}\).[3]
2. The maximum area is obtained when the value of \(x\), which can vary, gives a stationary value of \(A\). Find the maximum value of \(A\).[6]