Challenge Level

Three fences of lengths $p$, $q$ and $r$ with $p< q< r$ are arranged to form three sides $AB$, $BC$ and $CD$ of a field $ABCD$ with right angles at $B$ and $C$.

The diagram shows one possibility but the fences can be exchanged to make different enclosures.

The enclosure is completed by joining $A$ and $D$.

How should the rods be arranged to make the area of the enclosure as big as possible?