2014 Fermat Problem 9

In the diagram, PQRS is a square with side length 8. Points T and U are on PS and QR respectively with QU = TS = 1. The length of TU is closest to

\textbf{(A)}\ 8.5\quad \textbf{(B)}\ 9.9\quad \textbf{(C)}\ 10\quad \textbf{(D)}\ 10.6\quad \textbf{(E)}\ 11.3

If there are no answer choices shown, enter a numerical answer.

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