2013 Cayley Problem 9

In the diagram, \triangle PQR has a right angle at Q. A square is drawn on each side of the triangle. The area of the square on side QR is 144. The area of the square on side PR is 169. What is the area of the square on side PQ?

\textbf{(A)}\ 16\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 13\quad \textbf{(D)}\ 36\quad \textbf{(E)}\ 25

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.