3

Points $A$ and $B$ lie on the circumference of a circle of radius $r$ cm with centre at $O$.
The sector $OAB$ is shown in the diagram below. The angle $\angle AÔB$ is denoted as $\theta$ and is measured in radians.

The perimeter of the sector is $10$ cm and the area of the sector is $6.25$ cm².

(a) Show that $4r^{2}-20r+25=0$.

(b) Hence, or otherwise, find the value of $r$ and the value of $\theta$.