SAT Question e9c5bfb2: Area and Volume answer and explanation with Desmos solution

Choice B is correct. It’s given that rectangles $ABCD$ and $QRST$ are similar, where $A$, $B$, $C$, and $D$ correspond to $Q$, $R$, $S$, and $T$, respectively. It follows that $\overline{AB}$ corresponds to $\overline{QR}$ and $\overline{AD}$ corresponds to $\overline{QT}$. If two rectangles are similar, then the lengths of their corresponding sides are proportional. It’s given in the figure that the length of $\overline{AB}$ is $12$ inches, the length of $\overline{QR}$ is $5$ inches, and the length of $\overline{QT}$ is $10$ inches. If $x$ is the length, in inches, of $\overline{AD}$, then $\frac{12}{5}$ is equivalent to $\frac{x}{10}$. Therefore, the value of $x$ can be found using the equation $\frac{12}{5}=\frac{x}{10}$. Multiplying each side of this equation by $10$ yields $\frac{120}{5}=x$, or $24=x$. Therefore, the length, in inches, of $\overline{AD}$ is $24$.