2009 Cayley Problem 16

Rectangle PQRS is divided into eight squares, as shown. The side length of each shaded square is 10. What is the length of the side of the largest square?

\textbf{(A)}\ 18\quad \textbf{(B)}\ 24\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 23\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.