Question

△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 pair of known corresponding sides $AB = 2$ and $PQ=16$. The scale - factor $k=\frac{PQ}{AB}=\frac{16}{2} = 8$.

Step2: Calculate the missing side

The side $BC$ corresponds to $QR$. We know that $\frac{QR}{BC}=k$. Given $QR = 48$ and $k = 8$, then $BC=\frac{QR}{k}$. So $BC=\frac{48}{8}=6$.

Answer:

6