Triangles $PQR$ and $XYZ$ are **similar**, with the vertices in corresponding order. If $PQ = 6$, $PR = 4$, and $XY = 9$, what is the length of side $XZ$?

Similar triangles have corresponding sides in equal ratio. The vertex order $PQR \sim XYZ$ tells us $PQ \leftrightarrow XY$ and $PR \leftrightarrow XZ$. Scale factor from $PQR$ to $XYZ$: $\dfrac{XY}{PQ} = \dfrac{9}{6} = \dfrac{3}{2}$. Apply the scale to $PR$: $XZ = PR \cdot \dfrac{3}{2} = 4 \cdot \dfrac{3}{2} = 6$. - Trap A ($3 = 4 \cdot 3/4$) inverts the scale. - Trap B ($4.5$) uses scale factor $9/8$ or similar. - Trap D ($13.5 = 9 \cdot 1.5$) misapplies the scale to the wrong side. Check: ratio $\dfrac{XZ}{PR} = \dfrac{6}{4} = \dfrac{3}{2}$ matches $\dfrac{XY}{PQ} = \dfrac{9}{6} = \dfrac{3}{2}$ ✓.