1984 AHSME Problem 26

In the obtuse triangle ABC, AM=MB, MD\perp BC, EC\perp BC. If the area of \triangle ABC is 24, then the area of \triangle BED is

\mathrm{(A) \ }9 \qquad \mathrm{(B) \ }12 \qquad \mathrm{(C) \ } 15 \qquad \mathrm{(D) \ }18 \qquad \mathrm{(E) \ } \text{not uniquely determined}

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