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Solve similar triangles (advanced)

Problem

Solve for x.
x=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
Two triangles A B C and A D E. Triangle A B C is on top of Triangle A D E at point A. Side A C is smaller than A E and side A B is smaller than side A D. Side C B has a length of two. Side E D has a length of eleven. Side A B has a length of three. Segment B D has a length of x. Angle A B C and A D E are both ninety degrees.
Stuck?
Stuck?