Question

Given that

Triangle 1: 3 cm, 3 cm, 4 cm

Triangle 2: 6 cm, 6 cm, 8 cm

Triangle 3: 12 cm, 12 cm, 16 cm

Triangle 4: 24 cm, 24 cm, 32 cm

If Triangle 1 is the original triangle, what scale factor is used to generate Triangle 2, Triangle 3, and Triangle 4 from Triangle 1?

• A. Triangle 2: scale factor = 3
  Triangle 3: scale factor = 2
  Triangle 4: scale factor = 8
• B. Triangle 2: scale factor = 2
  Triangle 3: scale factor = 3
  Triangle 4: scale factor = 6
• C. Triangle 2: scale factor = 2
  Triangle 3: scale factor = 4
  Triangle 4: scale factor = 6
• D. Triangle 2: scale factor = 2
  Triangle 3: scale factor = 4
  Triangle 4: scale factor = 8

Answer 1

The correct option is D

Triangle 2: scale factor = 2
Triangle 3: scale factor = 4
Triangle 4: scale factor = 8

Ratio of sides of triangle 2 to triangle 1

$\frac{6}{3}=\frac{6}{3}=\frac{8}{4}=2$

Ratio of sides of triangle 3 to triangle 1

$\frac{12}{3}=\frac{126}{3}=\frac{16}{4}=4$

Ratio of sides of triangle 4 to triangle 1

$\frac{24}{3}=\frac{24}{3}=\frac{32}{4}=8$