This one has been eating at me for a long time and I just can't figure it out:

In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

How do I show/prove that it's 10 meters?