9.
Diagram NOT accurately drawn
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0b4165d-b8bb-419c-b75a-d6c0c2431510-24_581_1491_340_296}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows the plan view of the area being used for a ball-throwing competition.
Competitors must stand within the circle \(C\) and throw a ball as far as possible into the target area, \(P Q R S\), shown shaded in Figure 3.
Given that
- circle \(C\) has centre \(O\)
- \(P\) and \(S\) are points on \(C\)
- \(O P Q R S O\) is a sector of a circle with centre \(O\)
- the length of arc \(P S\) is 0.72 m
- the size of angle \(P O S\) is 0.6 radians
- show that \(O P = 1.2 \mathrm {~m}\)
Given also that
- the target area, \(P Q R S\), is \(90 \mathrm {~m} ^ { 2 }\)
- length \(P Q = x\) metres
- show that
$$5 x ^ { 2 } + 12 x - 1500 = 0$$
Hence calculate the total perimeter of the target area, \(P Q R S\), giving your answer to the nearest metre.