3.13: Sector perimeter minimised for fixed area

In this question lengths are in centimetres and angles are in radians.

The diagram shows a circle with centre $O$ and radius $r$. The points $A$ and $B$ lie on the circumference of the circle. The area of the minor sector $OAB$ is $25\text{ cm}^{2}$. The angle $AOB$ is $\theta$.