2010 Pascal Problem 22

Rhombus PQRS is inscribed in rectangle JKLM, as shown. (A *rhombus* is a quadrilateral with four equal side lengths.) Segments PZ and XR are parallel to JM. Segments QW and YS are parallel to JK. If JP = 39, JS = 52, and KQ = 25, what is the perimeter of rectangle WXYZ?

\textbf{(A)}\ 48\quad \textbf{(B)}\ 58\quad \textbf{(C)}\ 84\quad \textbf{(D)}\ 96\quad \textbf{(E)}\ 108

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 Pascal contests here.