The diagram shows the sector \(OPQ\) of a circle, centre \(O\), radius \(r\) cm, where angle \(POQ=\theta\) radians. The perimeter of the sector is \(10\) cm.

(i) Show that the area, \(A\text{ cm}^2\), of the sector is given by

\(A=\frac{50\theta}{(2+\theta)^2}.\)

It is given that \(\theta\) can vary and \(A\) has a maximum value.

(ii) Find the maximum value of \(A\).