Let $A B C D$ be a rectangle with its shorter side $a > 0$ units and perimeter $2 s$ units. Let $P Q R S$ be any rectangle such that vertices $A , B , C$ and $D$ respectively lie on the lines $P Q , Q R , R S$ and $S P$. Then the maximum area of such a rectangle $P Q R S$ in square units is given by\\
(A) $s ^ { 2 }$\\
(B) $2 a ( s - a )$\\
(C) $\frac { s ^ { 2 } } { 2 }$\\
(D) $\frac { 5 } { 2 } a ( s - a )$.