Geometry Basics · Superchallenge problem

A right triangle has legs $6$ and $8$. Square $X$ sits in the right-angle corner: two of its sides lie along the legs and its fourth corner touches the hypotenuse. Square $Y$ has one whole side lying on the hypotenuse, and its other two corners touch the two legs. What is the side of $X$ divided by the side of $Y$? Give your answer as a fraction in lowest terms.