2023 SCSS P1 Q10

The diagram shows a square \(PQRS\) of sides 8 cm each and a triangle \(PXY\). \(X\) and \(Y\) lie on \(QR\) and \(SR\) respectively, and \(XR=YR=k\) cm.

1. Show that the area, \(A\text{ cm}^2\), of triangle \(PXY\) is given by \(A=8k-\dfrac12k^2\).[3]
2. Given that \(k\) can vary, find the value of \(k\) for which there is a stationary value of \(A\) and calculate this value of \(A\).[5]
3. Determine whether this stationary value of \(A\) is a maximum or minimum value.[1]