AMC 10B 2011 Problem 9

The area of \triangle E B D is one third of the area of 3-4-5 \triangle A B C. Segment D E is perpendicular to segment A B. What is B D ?

Answer Choices
A. \dfrac{4}{3}
B. \sqrt{5}
C. \dfrac{9}{4}
D. \dfrac{4 \sqrt{3}}{3}
E. \dfrac{5}{2}

Image