Question

1. △stu~△pqr (find x)

x = __________

Explanation:

Step1: Set up proportion

Since $\triangle STU\sim\triangle PQR$, the ratios of corresponding sides are equal. So, $\frac{ST}{PQ}=\frac{SU}{PR}$.

Step2: Substitute values

We know that $ST = 6$, $PQ = 4$, and $SU=12$. Substituting into the proportion gives $\frac{6}{4}=\frac{12}{x}$.

Step3: Cross - multiply

Cross - multiplying gives $6x = 4\times12$.

Step4: Solve for x

$6x=48$, then $x=\frac{48}{6}=8$.

Answer:

$8$