16.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4b084faa-a680-4f35-bb5c-a4edf5171b5f-24_458_604_285_751}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows the plan view of the design for a swimming pool.
The shape of this pool \(A B C D E A\) consists of a rectangular section \(A B D E\) joined to a semicircular section \(B C D\) as shown in Figure 4.
Given that \(A E = 2 x\) metres, \(E D = y\) metres and the area of the pool is \(250 \mathrm {~m} ^ { 2 }\),
- show that the perimeter, \(P\) metres, of the pool is given by
$$P = 2 x + \frac { 250 } { x } + \frac { \pi x } { 2 }$$
- Explain why \(0 < x < \sqrt { \frac { 500 } { \pi } }\)
- Find the minimum perimeter of the pool, giving your answer to 3 significant figures.