2024 CJC H1 Q3

The diagram shows the layout of a rectangular sandpit of dimension \(x\) metres by \(y\) metres, inscribed in a triangular playground with height \(28\) metres and base \(20\) metres.

1. Show that the area, \(A\) \(\mathrm{m}^2\), of the sandpit is given by \(A = 28x - \frac{7}{5}x^2\).[2]
2. Using differentiation, find the maximum area of the sandpit as \(x\) varies. Show that the maximum area of the sandpit occupies \(\frac{1}{2}\) of the area of the playground.[5]