SMO 2006 Senior Round 1 Question 17

In the diagram below, $ABCD$ is a square. The points $A,B,G$ are collinear. Segments $AC$ and $DG$ intersect at $E$, and segments $DG$ and $BC$ intersect at $F$. Suppose $DE=15$ cm, $EF=9$ cm, and $FG=x$ cm. Find $x$.