1959 AHSME Problem 10

In \triangle ABC with \overline{AB}=\overline{AC}=3.6, a point D is taken on AB at a distance 1.2 from A. Point D is joined to E in the prolongation of AC so that \triangle AED is equal in area to ABC. Then \overline{AE} is: \textbf{(A)}\ 4.8 \qquad\textbf{(B)}\ 5.4\qquad\textbf{(C)}\ 7.2\qquad\textbf{(D)}\ 10.8\qquad\textbf{(E)}\ 12.6

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