Scale Factor Practice Problems

Name:

Date:

Scale factor diagram showing similar shapes

📐 Part 1: Finding Scale Factors

1. Rectangle A has a length of 4 cm and Rectangle B has a length of 12 cm. What is the scale factor from Rectangle A to Rectangle B?

Scale factor = _______

2. A model car is 15 cm long. The real car is 4.5 metres long. What is the scale factor from the model to the real car?

Scale factor = _______

3. Which of these represents a scale factor that makes shapes smaller?

Scale factor of 3

Scale factor of 0.5

Scale factor of 1.2

Scale factor of 2

4. Triangle X has sides of 6 cm, 8 cm, and 10 cm. Triangle Y has sides of 9 cm, 12 cm, and 15 cm. What is the scale factor from Triangle X to Triangle Y?

Scale factor = _______

🗺️ Part 2: Using Scale Factors

5. On a map, the scale factor is 1:50,000. If two towns are 8 cm apart on the map, what is the real distance between them?

Real distance = _______ km

6. A photograph is enlarged with a scale factor of 1.5. If the original photo was 10 cm wide, how wide is the enlarged photo?

New width = _______ cm

7. A garden plan uses a scale factor of 1:20. If a flower bed is shown as 3 cm long on the plan, what is its real length?

Real length = _______ cm

💭 Part 3: Problem Solving

8. A dollhouse is built using a scale factor of 1:12. If the real door is 2.1 metres tall, how tall should the dollhouse door be? Give your answer in centimetres.

Dollhouse door height = _______ cm

9. Explain in your own words what a scale factor tells us about the relationship between two similar shapes.

10. A shape is enlarged by a scale factor of 2.5. If one side of the original shape is 4.8 cm, what is the length of the corresponding side in the enlarged shape?

New side length = _______ cm