Triangle abc is similar to fbe.

=> be/bc = ef/ac = dc/ac = 2

Triangle abc is similar to ade.

ac/ec = bc/dc. Let da = ac = x.

x/ec = bc/2x

2x^2 = ec * bc. Let bc=y => be=2y => ec=3y => 2x^2 = 3y^2.

One last thing, from Pithagoras:

(2x)^2 + 5^2 = (3y)^2. Both should give you the solution.

Not very hard, but need to be careful.

-O