CEMC Cayley, 2004

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, $ABCDEFG$ is a room having square corners, with $EF=20$ m, $AB=10$ 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 $D$ ?

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

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