Question

1. if the figures below are similar, find the scale factor of figure b to figure a.

figure a: a triangle with sides 27, 48, 60
figure b: a triangle with sides 16, 20, 9

Explanation:

Step1: Identify corresponding sides

First, we need to match the corresponding sides of the similar triangles. Let's list the side lengths:

• Triangle A: 27, 48, 60
• Triangle B: 9, 16, 20

We can see that 27 corresponds to 9, 48 corresponds to 16, and 60 corresponds to 20 (since \( \frac{27}{9} = 3 \), \( \frac{48}{16} = 3 \), \( \frac{60}{20} = 3 \), but we need the scale factor of B to A, so we take the ratio of a side of B to the corresponding side of A).

Step2: Calculate the scale factor

The scale factor of B to A is the ratio of a side length of B to the corresponding side length of A. Let's take the side of length 9 in B and the corresponding side of length 27 in A:
\( \text{Scale factor} = \frac{\text{Side of B}}{\text{Corresponding side of A}} = \frac{9}{27} = \frac{1}{3} \) (we can check with other sides: \( \frac{16}{48} = \frac{1}{3} \), \( \frac{20}{60} = \frac{1}{3} \), so it's consistent).

Answer:

\( \frac{1}{3} \)