SAT Question 51f26ce8: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. The figure shows that angle $P$ in $△QPR$ and angle $T$ in $△STR$ are right angles. It follows that angle $P$ is congruent to angle $T$. The figure also shows that the measures of angle $QRP$ and angle $SRT$ are both $x^{\circ }$. Therefore, angle $QRP$ is congruent to angle $SRT$. It's given that $△QPR$ is similar to $△STR$. Since angle $P$ is congruent to angle $T$, and angle $QRP$ is congruent to angle $SRT$, it follows that $\overline{QR}$ corresponds to $\overline{SR}$, and $\overline{QP}$ corresponds to $\overline{ST}$. Since corresponding sides of similar triangles are proportional, it follows that $\frac{SR}{QR}=\frac{ST}{QP}$. It's also given that the lengths of $\overline{ST}$, $\overline{QP}$, and $\overline{QR}$ are $14$, $15$, and $25$, respectively. Substituting $14$ for $ST$, $15$ for $QP$, and $25$ for $QR$ in the equation $\frac{SR}{QR}=\frac{ST}{QP}$ yields $\frac{SR}{25}=\frac{14}{15}$. Multiplying each side of this equation by $25$ yields $SR=\left(\frac{14}{15}\right)\left(25\right)$, or $SR=\frac{350}{15}$. Thus, the length of $\overline{SR}$ is $\frac{350}{15}$.