Senior Mathematical Challenge 2017 Q15

The diagram shows a square $PQRS$. Points $T$, $U$, $V$ and $W$ lie on the edges of the square as shown, such that $PT=1$, $QU=2$, $RV=3$ and $SW=4$. The area of $TUVW$ is half that of $PQRS$.

What is the length of $PQ$?