SAT Question e0874bc2: Area and Volume answer and explanation with Desmos solution

Choice D is correct. It's given that triangle $XYZ$ is similar to triangle $TUV$. Therefore, each side of triangle $XYZ$ is $k$ times its corresponding side of triangle $TUV$, where $k$ is a constant. It follows that the perimeter of triangle $XYZ$ is $k$ times the perimeter of triangle $TUV$. It's also given that $\overline{TU}$ corresponds to $\overline{XY}$ and the length of $\overline{TU}$ is $18$. Let $x$ represent the length of $\overline{XY}$. It follows that $x=18k$. The table shows that the perimeters of triangles $TUV$ and $XYZ$ are $37$ and $333$, respectively. It follows that $333=37k$, or $9=k$. Substituting $9$ for $k$ in the equation $x=18k$ yields $x=\left(18\right)\left(9\right)$, or $x=162$. Therefore, the length of $\overline{XY}$ is $162$.