Square $EFGH$ has one vertex on each side of square $ABCD$. Point $E$ is on $\overline{AB}$ with $AE=3\cdot EB$. What is the ratio of the area of $EFGH$ to the area of $ABCD$?

1. Let $AH=BE=x, AE=3x$. Then $HE^2=x^2+9x^2=10x^2, [ABCD]=16x^2$.
2. So the ratio is $10:16=5:8$.