2008 Fermat Problem 19

In the diagram, R is on QS and QR = 8. Also, PR = 12, \angle PRQ = 120^\circ, and \angle RPS = 90^\circ. What is the area of \triangle QPS?

\textbf{(A)}\ 72\sqrt{3}\quad \textbf{(B)}\ 72\quad \textbf{(C)}\ 36\quad \textbf{(D)}\ 60\sqrt{3}\quad \textbf{(E)}\ 96\sqrt{3}

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