Answer: $\frac{28}{9}$
51. As shown in the figure, squares $A B C D$ and $B E F G$ with side lengths of 4 cm and 3 cm, respectively, are placed side by side. $A F$ intersects $B G$ at $P$, then the ratio of the area of $\triangle A P E$ to the area of $\triangle G F P$ is $\qquad$.