2003 AMC 12B Problem 14

In rectangle ABCD, AB=5 and BC=3. Points F and G are on \overline{CD} so that DF=1 and GC=2. Lines AF and BG intersect at E. Find the area of \triangle AEB.

\text {(A) } 10 \qquad \text {(B) } \frac{21}{2} \qquad \text {(C) } 12 \qquad \text {(D) } \frac{25}{2} \qquad \text {(E) } 15

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