2007 Fermat Problem 22

A ball placed at point P on a rectangular billiard table is shot at an angle of 45^\circ to the edge of the table. After successively bouncing off the edges of the table at 45^\circ angles, it returns to point P, as shown. If the ball travels 7 m, the perimeter, in metres, of the table is closest to

\textbf{(A)}\ 7.0\quad \textbf{(B)}\ 7.5\quad \textbf{(C)}\ 8.0\quad \textbf{(D)}\ 8.5\quad \textbf{(E)}\ 9.0

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 Fermat contests here.