AMC 12 2003b 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 $\triangle AEB$.

File:Problem_14.png

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