SAT Question fc5ef8d3: Area and Volume answer and explanation with Desmos solution

Choice C is correct. It's given that triangle $TUV$ is similar to triangle $XYZ$, and $\overline{TU}$ corresponds to $\overline{XY}$. If two triangles are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides. It's given that the perimeter of triangle $TUV$ is $50$, the perimeter of triangle $XYZ$ is $150$, and the length of $\overline{TU}$ is $6$. Let $n$ represent the length of $\overline{XY}$. It follows that $\frac{50}{150}=\frac{6}{n}$, or $\frac{1}{3}=\frac{6}{n}$. Multiplying each side of this equation by $n$ yields $\frac{n}{3}=6$. Multiplying each side of this equation by $3$ yields $n=18$. Therefore, the length of $\overline{XY}$ is $18$.