Diagram 5 shows a wire frame.The length of the wire is 60 cm and the radius of the semicircle is $\displaystyle r cm$

(i)show that the area of the frame,$\displaystyle L cm^2,$ is given by $\displaystyle L=60r-2r^2-\frac{1}{2}\pi r^2$

(ii)Hence,calculate the maximum area of the frame