Question

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

Explanation:

Step1: Find the scale - factor

Since the triangles are similar, the ratios of corresponding sides are equal. Let's find the scale - factor using the known corresponding sides. $\frac{PQ}{AB}=\frac{28}{4} = 7$.

Step2: Calculate the missing side

The side corresponding to the missing side in $\triangle ABC$ is $QR$ in $\triangle PQR$. Let the missing side of $\triangle ABC$ be $x$. Then $\frac{QR}{x}=7$. We know $QR = 56$, so $x=\frac{56}{7}=8$.

Answer:

8