jmc

Since $△XYZ$ is a right triangle with $\angle X=90^{\circ }$, we have $\tan Z=\frac{XY}{XZ}$. Since $\tan Z=7$, we have $XY=7k$ and $XZ=k$ for some value of $k$, as shown in the diagram. Applying the Pythagorean Theorem gives $(7k{)}^2+k^2=100^2$, so $50k^2=100^2$, which gives $k^2=100^2/50=200$. Since $k$ must be positive, we have $k=\sqrt{200}=10\sqrt{2}$, so $XY=7k=\boxed{70\sqrt{2}}$.