2004 Cayley Problem 22

In the diagram, ABCDEFG is a room having square corners, with EF = 20\text{ m}, AB = 10\text{ m}, and AG = GF. The total area of the room is 280\text{ m}^2. A wall is built from A to D creating two rooms of equal area. What is the distance, in metres, from C to D?

\textbf{(A)}\ 15\quad \textbf{(B)}\ \frac{50}{3}\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 13\quad \textbf{(E)}\ \frac{40}{3}

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 Cayley contests here.