8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{42116a65-60ec-4dff-a05e-bab529939e1e-11_403_440_262_744}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a flowerbed. Its shape is a quarter of a circle of radius \(x\) metres with two equal rectangles attached to it along its radii. Each rectangle has length equal to \(x\) metres and width equal to \(y\) metres.
Given that the area of the flowerbed is \(4 \mathrm {~m} ^ { 2 }\),
- show that
$$y = \frac { 16 - \pi x ^ { 2 } } { 8 x }$$
- Hence show that the perimeter \(P\) metres of the flowerbed is given by the equation
$$P = \frac { 8 } { x } + 2 x$$
- Use calculus to find the minimum value of \(P\).
- Find the width of each rectangle when the perimeter is a minimum. Give your answer to the nearest centimetre.