2013 Fermat Problem 10

PQRS is a square. The midpoint of PQ is M and the midpoint of RS is N. If the perimeter of rectangle PMNS is 36, the area of square PQRS is

\textbf{(A)}\ 81\quad \textbf{(B)}\ 72\quad \textbf{(C)}\ 324\quad \textbf{(D)}\ 144\quad \textbf{(E)}\ 36

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Full credit to this problem is given to the CEMC, you may view all Fermat contests here.