2024 Cayley Problem 13

In the diagram, quadrilateral ABCD has AB = 20, BC = 12, and CD = 15. Also, AB and CD are perpendicular to BC. The perimeter of quadrilateral ABCD is

\textbf{(A)}\ 47\quad \textbf{(B)}\ 59\quad \textbf{(C)}\ 84\quad \textbf{(D)}\ 72\quad \textbf{(E)}\ 60

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.