Triangle A B C is similar to triangle X Y Z , where A , B

Choice D is correct. It's given that triangle $ABC$ is similar to triangle $XYZ$, where $A$, $B$, and $C$ correspond to $X$, $Y$, and $Z$, respectively. It follows that side $AB$ corresponds to side $XY$ and side $BC$ corresponds to side $YZ$. Since the lengths of corresponding sides in similar triangles are proportional, it follows that $\frac{XY}{AB}=\frac{YZ}{BC}$. Substituting $170$ for $AB$, $60$ for $YZ$, and $850$ for $BC$ in this equation yields $\frac{XY}{170}=\frac{60}{850}$. Multiplying each side of this equation by $170$ yields $XY=12$. Therefore, the length of $\overline{XY}$ is $12$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the length of $\overline{YZ}$, not $\overline{XY}$.