5 The diagram shows a sector \(A O B\) of a circle with centre \(O\) and radius \(r \mathrm {~cm}\).
\includegraphics[max width=\textwidth, alt={}, center]{66b1c52c-0475-493a-8c0a-abf4c2c7b07d-06_414_584_516_863}
The angle \(A O B\) is \(\theta\) radians
The sector has area \(9 \mathrm {~cm} ^ { 2 }\) and perimeter 15 cm .
5
- Show that \(r\) satisfies the equation \(2 r ^ { 2 } - 15 r + 18 = 0\)
[0pt]
[4 marks]
5 - Find the value of \(\theta\). Explain why it is the only possible value.
[0pt]
[4 marks]