SAT Question babd7461: Area and Volume answer and explanation with Desmos solution

Choice A is correct. It's given that triangle $JKL$ is similar to triangle $RST$, where $J$ corresponds to $R$ and $K$ corresponds to $S$. It follows that $\overline{JK}$ corresponds to $\overline{RS}$. If two triangles are similar, then the scale factor between their perimeters is equal to the scale factor between the lengths of their corresponding sides. It's given that the length of $\overline{JK}$ is $15$ and the length of $\overline{RS}$ is $135$. Therefore, the scale factor from the length of $\overline{JK}$ to the length of $\overline{RS}$ is $\frac{135}{15}$, or $9$. It's given that the perimeter of triangle $JKL$ is $36$. Let $p$ represent the perimeter of triangle $RST$. It follows that $\frac{p}{36}=9$. Multiplying each side of this equation by $36$ yields $p=324$. Therefore, the perimeter of triangle $RST$ is $324$.