△abc and △pqr are similar. find the missing side length. (the triangles are not drawn to scale.)

Explanation:

Step1: Find the scale - factor

The ratio of corresponding sides of similar triangles is the same. Consider the sides $AB = 12$ and $PQ = 2$. The scale - factor $k=\frac{PQ}{AB}=\frac{2}{12}=\frac{1}{6}$.

Step2: Find the missing side

The side corresponding to the missing side in $\triangle PQR$ in $\triangle ABC$ is $BC = 30$. Let the missing side be $x$. Then, using the scale - factor, we have $x = BC\times k$. Substituting the values, $x=30\times\frac{1}{6}=5$.

Answer:

5