The area of $\triangle$$EBD$ is one third of the area of $3-4-5$ $\triangle$$ABC$. Segment $DE$ is perpendicular to segment $AB$. What is $BD$?
$\textbf{(A)}\ \frac{4}{3} \qquad$ $\textbf{(B)}\ \sqrt{5} \qquad$ $\textbf{(C)}\ \frac{9}{4} \qquad$ $\textbf{(D)}\ \frac{4\sqrt{3}}{3} \qquad$ $\textbf{(E)}\ \frac{5}{2}$