AHSME 1961 Problem 10

Each side of $\triangle ABC$ is $12$ units. $D$ is the foot of the perpendicular dropped from $A$ on $BC$, and $E$ is the midpoint of $AD$. The length of $BE$, in the same unit, is: $\textbf{(A)}\ \sqrt{18} \textbf{(B)}\ \sqrt{28} \textbf{(C)}\ 6 \textbf{(D)}\ \sqrt{63} \textbf{(E)}\ \sqrt{98}$