Questions on Proportions to Find Scale Factor
Multiple-choice questions (MCQs) focused on Proportions to Find Scale Factor, each with five alternatives (A–E). These questions help learners understand how to determine the scale factor between two similar shapes using proportions.
20 Multiple-Choice Questions: Proportions to Find Scale Factor
1. A triangle has a side of 6 cm, and a similar triangle has the corresponding side of 18 cm. What is the scale factor from the smaller to the larger triangle?
A) 1:2
B) 1:3
C) 1:4
D) 2:3
E) 3:1
2. A rectangle is enlarged so that its length goes from 5 cm to 20 cm. What is the scale factor of the enlargement?
A) 1:2
B) 2:1
C) 3:1
D) 4:1
E) 1:4
3. A small model is 10 cm long, and the real object is 40 cm long. What is the scale factor from the model to the real object?
A) 1:2
B) 1:3
C) 1:4
D) 1:5
E) 1:6
4. Two similar rectangles have widths of 8 inches and 12 inches. What is the scale factor from the smaller to the larger rectangle?
A) 2:3
B) 3:2
C) 4:3
D) 5:3
E) 3:4
5. The scale factor from a small square to a larger square is 3:5. If the side of the smaller square is 6 cm, what is the side of the larger square?
A) 8 cm
B) 9 cm
C) 10 cm
D) 12 cm
E) 15 cm
6. A rectangle of 9 cm width is reduced to a width of 3 cm. What is the scale factor from the original to the reduced figure?
A) 1:2
B) 1:3
C) 1:4
D) 2:3
E) 3:1
7. A model’s height is 15 cm, and it represents an object 60 cm tall. What is the scale factor?
A) 1:2
B) 1:3
C) 1:4
D) 1:5
E) 1:6
8. A triangle is scaled from 12 cm to 36 cm. What is the scale factor?
A) 1:4
B) 1:3
C) 1:2
D) 1:5
E) 3:1
9. A rectangle is reduced from 24 cm to 8 cm. What is the scale factor of the reduction?
A) 3:1
B) 1:3
C) 1:2
D) 1:4
E) 1:6
10. Two circles have radii of 5 cm and 15 cm. What is the scale factor from the smaller to the larger?
A) 1:2
B) 1:3
C) 2:3
D) 3:1
E) 5:15
11. If a figure is enlarged using a scale factor of 2:5, and its original height is 8 cm, what is the new height?
A) 10 cm
B) 18 cm
C) 19 cm
D) 20 cm
E) 22 cm
12. A photo measuring 3 inches by 4 inches is enlarged to 9 inches wide. What is the scale factor?
A) 1:2
B) 1:3
C) 3:1
D) 2:3
E) 3:4
13. A rectangle with length 14 cm is scaled down to 7 cm. What is the scale factor?
A) 1:2
B) 2:1
C) 1:3
D) 1:4
E) 1:5
14. A model of a bridge is built at a scale of 1:50. If the model is 2 meters long, how long is the real bridge?
A) 25 m
B) 50 m
C) 75 m
D) 100 m
E) 120 m
15. Two similar hexagons have sides of 9 cm and 27 cm. What is the scale factor from the smaller to the larger?
A) 1:2
B) 1:3
C) 2:3
D) 3:2
E) 3:1
16. A building is 200 feet tall, and a model of it is 10 feet tall. What is the scale factor from the model to the building?
A) 1:5
B) 1:10
C) 1:15
D) 1:20
E) 1:25
17. A square of area 36 cm² is scaled to a square of area 144 cm². What is the linear scale factor?
A) 2
B) 3
C) 4
D) 6
E) 12
18. A poster’s width changes from 18 inches to 6 inches. What is the scale factor of the reduction?
A) 1:2
B) 2:3
C) 1:3
D) 3:1
E) 1:4
19. A figure with length 16 cm is scaled by a factor of 3:2. What is the new length?
A) 12 cm
B) 18 cm
C) 20 cm
D) 22 cm
E) 24 cm
20. If a blueprint uses a scale of 1 cm : 4 meters, what is the scale factor from the blueprint to the real building?
A) 1:2
B) 1:4
C) 1:40
D) 1:400
E) 1:10
Answer Key with Explanations
1. B) 1:3
6 cm to 18 cm → 6:18 = 1:3
2. D) 4:1
5 to 20 → 20 ÷ 5 = 4
3. C) 1:4
10 to 40 → 10:40 = 1:4
4. A) 2:3
8:12 = 2:3
5. C) 10 cm
6 × 5/3 = 10
6. B) 1:3
3/9 = 1:3
7. C) 1:4
15 to 60 = 1:4
8. B) 1:3
12 to 36 → 12:36 = 1:3
9. D) 1:3
8:24 = 1:3
10. B) 1:3
5:15 = 1:3
11. D) 20 cm
8 × (5/2) = 20
12. B) 1:3
3 to 9 → 1:3
13. A) 1:2
7:14 = 1:2
14. D) 100 m
2 × 50 = 100
15. B) 1:3
9:27 = 1:3
16. E) 1:20
10:200 = 1:20
17. A) 2
√144 = 12, √36 = 6 → 6:12 = 1:2 → scale factor = 2
18. C) 1:3
6:18 = 1:3
19. E) 24 cm
20. B) 1:4
1 cm : 4 m → scale factor = 1:4
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