8. (5 points) As shown in the figure, in square $A B C D$, point $E$ is on side $A D$, and point $F$ is on side $D C$, with $A E=2 E D$ and $D F=3 F C$. The ratio of the area of $\triangle B E F$ to the area of square $A B C D$ is $\qquad$ .
【Solution】Solution: According to the problem, we have:
Let the side length of the square be 12. The area of the square is $12 \times 12=144$. The area of the shaded part is: $S=144-\frac{1}{2}(12 \times 8+4 \times 9+3 \times 12)=60$. The ratio of the area of $\triangle B E F$ to the area of square $A B C D$ is $60: 144$, which simplifies to $5: 12$. Therefore, the answer is: $\frac{5}{12}$.