2017 AMC 10B Problem 15

Rectangle ABCD has AB=3 and BC=4. Point E is the foot of the perpendicular from B to diagonal \overline{AC}. What is the area of \triangle AED?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ \frac{42}{25}\qquad\textbf{(C)}\ \frac{28}{15}\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{54}{25}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.