Question

part a consider the similar triangles below: find the scale factor? part b find the length of side pr?

Explanation:

Step1: Identify corresponding sides

Let's assume $\triangle ABC\sim\triangle PQR$. The side corresponding to $BC = 6$ is $QR=12$.

Step2: Calculate scale - factor

The scale factor $k$ from $\triangle ABC$ to $\triangle PQR$ is found by dividing the length of a side of $\triangle PQR$ by the length of the corresponding side of $\triangle ABC$. So, $k=\frac{QR}{BC}=\frac{12}{6} = 2$.

Step3: Find length of $PR$

Since the scale factor is $2$ and the side corresponding to $PR$ in $\triangle ABC$ is $AC = 7$, then $PR=k\times AC$. Substituting $k = 2$ and $AC = 7$, we get $PR=2\times7=14$.

Answer:

Part A: 2
Part B: 14