2022 Cayley Problem 16

In the diagram, hexagon PQRSTU has interior right angles at P, Q, S, T, and U and an exterior right angle at R. Also, PU = UT, PQ = ST = 10, and QS = 8. The perimeter of PQRSTU is closest to

\textbf{(A)}\ 48\quad \textbf{(B)}\ 56\quad \textbf{(C)}\ 63\quad \textbf{(D)}\ 71\quad \textbf{(E)}\ 72

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.