2016 Pascal Problem 12

In the diagram, the area of square QRST is 36. Also, the length of PQ is one-half of the length of QR. What is the perimeter of rectangle PRSU?

\textbf{(A)}\ 24\quad \textbf{(B)}\ 30\quad \textbf{(C)}\ 90\quad \textbf{(D)}\ 45\quad \textbf{(E)}\ 48

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