2016 Cayley Problem 11

In the diagram, PQ is perpendicular to QR, QR is perpendicular to RS, and RS is perpendicular to ST. If PQ = 4, QR = 8, RS = 8, and ST = 3, then the distance from P to T is

\textbf{(A)}\ 16\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 17\quad \textbf{(D)}\ 15\quad \textbf{(E)}\ 13

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.