Question

3
part a
consider the similar triangles below:

find the scale factor?

part b
find the length of side pr ?

Explanation:

Part A

Step1: Identify corresponding sides

Corresponding sides: \( BC = 6 \) and \( QR = 12 \) (since the triangles are similar, the sides around the equal angles correspond).

Step2: Calculate scale factor

Scale factor is the ratio of the length of a side in the larger triangle to the corresponding side in the smaller triangle. So, scale factor \( = \frac{12}{6} = 2 \).

Step1: Identify corresponding side

In triangle \( ABC \), side \( AC = 7 \) corresponds to side \( PR \) in triangle \( PQR \).

Step2: Apply scale factor

Since the scale factor is 2 (from Part A), the length of \( PR \) is the length of \( AC \) multiplied by the scale factor. So, \( PR = 7 \times 2 = 14 \).

Answer:

2

Part B