Australian AMC 2015 - Senior Question 29

In a $38\times 32$ rectangle $ABCD$, points $P$, $Q$, $R$ and $S$ are chosen, one on each side of $ABCD$ as pictured. The lengths $AP$, $PB$, $BQ$, $QC$, $CR$, $RD$, $DS$ and $SA$ are all positive integers and $PQRS$ is a rectangle.

What is the largest possible area that $PQRS$ could have?