imc

Let $8s$ be the length of the sides of square $ABCD$, then the length of one of the sides of square $EFGH$ is $\sqrt{(7s{)}^2+s^2}=\sqrt{50s^2}$, and hence the ratio in the areas is $\frac{{\sqrt{50s^2}}^2}{(8s{)}^2}=\frac{50}{64}=\boxed{\frac{25}{32}}$.