Questions about Proportions to Find Dimensions
Multiple-choice questions about Proportions to Find Dimensions, each with five alternatives (A–E). These problems are designed to practice using proportions to find missing lengths, widths, heights, or other dimensions when scaling up or down figures like rectangles, photos, maps, or models.
The answers with full explanations follow the questions.
Proportions to Find Dimensions – Multiple-Choice Questions
1. A rectangle has a length of 10 cm and a width of 4 cm. What is the width of a similar rectangle with a length of 25 cm?
A) 6 cm
B) 8 cm
C) 9 cm
D) 10 cm
E) 12 cm
2. A model car is 5 inches long and 2 inches wide. What would be the width of a full-size car that is 15 feet long, assuming the same proportions?
A) 4 ft
B) 5 ft
C) 6 ft
D) 7 ft
E) 8 ft
3. A photo measuring 6 inches by 4 inches is enlarged to a width of 10 inches. What is the new height?
A) 5 in
B) 6.5 in
C) 6 in
D) 7 in
E) 8 in
4. A map scale shows 1 inch = 20 miles. How many miles does 2.5 inches represent?
A) 40
B) 45
C) 50
D) 55
E) 60
5. A triangle with base 6 cm and height 8 cm is enlarged so the new base is 15 cm. What is the new height?
A) 18
B) 20
C) 21
D) 22
E) 24
6. A room that is 12 feet long is represented by a model that is 3 inches long. What is the scale of the model?
A) 1 in = 2 ft
B) 1 in = 3 ft
C) 1 in = 4 ft
D) 1 in = 5 ft
E) 1 in = 6 ft
7. A painting is 18 inches tall and 12 inches wide. A reduced copy is 6 inches wide. What is the height?
A) 6
B) 7
C) 8
D) 9
E) 10
8. A rectangular photo 5 cm wide is enlarged proportionally to a width of 15 cm. Its original height is 7 cm. What is the new height?
A) 18
B) 19
C) 20
D) 21
E) 22
9. A model airplane is 10 inches long. If the real airplane is 80 feet long, what is the scale?
A) 1 in = 6 ft
B) 1 in = 7 ft
C) 1 in = 8 ft
D) 1 in = 9 ft
E) 1 in = 10 ft
10. A scale model of a building is 30 inches tall and represents a real building 150 feet tall. What is the scale?
A) 1 in = 3 ft
B) 1 in = 4 ft
C) 1 in = 5 ft
D) 1 in = 6 ft
E) 1 in = 7 ft
11. A rectangle has a width of 5 cm and a length of 12 cm. What is the width of a similar rectangle with a length of 24 cm?
A) 8 cm
B) 9 cm
C) 10 cm
D) 11 cm
E) 12 cm
12. On a map, 3 inches represent 60 miles. How many inches represent 100 miles?
A) 4 in
B) 4.5 in
C) 5 in
D) 5.5 in
E) 6 in
13. A triangle has sides 9 cm, 12 cm, and 15 cm. If enlarged by a scale factor of 2, what is the length of the longest side?
A) 25
B) 28
C) 30
D) 32
E) 35
14. A miniature statue is 7 inches tall and is a 1:12 scale model. What is the height of the real statue?
A) 70 in
B) 75 in
C) 80 in
D) 84 in
E) 90 in
15. A poster is scaled down from 36 inches wide to 18 inches wide. Its original height was 48 inches. What is the reduced height?
A) 22
B) 24
C) 26
D) 28
E) 30
16. A blueprint has a room that measures 5 inches. If the scale is 1 inch = 4 feet, how long is the actual room?
A) 18 ft
B) 19 ft
C) 20 ft
D) 21 ft
E) 22 ft
17. A rectangle has length 9 and width 6. What is the width of a similar rectangle with length 18?
A) 10
B) 11
C) 12
D) 13
E) 14
18. A model building is 8 inches tall and represents a 64-foot-tall building. What is the scale?
A) 1 in = 6 ft
B) 1 in = 7 ft
C) 1 in = 8 ft
D) 1 in = 9 ft
E) 1 in = 10 ft
19. A 6-inch toy figure is a 1:12 scale of a real person. How tall is the real person in inches?
A) 60
B) 66
C) 70
D) 72
E) 75
20. A scale drawing uses a scale of 1 cm = 5 meters. If a building is 60 meters tall, how tall will it be in the drawing?
A) 10 cm
B) 11 cm
C) 12 cm
D) 13 cm
E) 14 cm
Answers with Explanations
1. D) 10 cm
Proportion: 10/4 = 25/x → 10x = 100 → x = 10
2. C) 6 ft
Proportion: 5/2 = 15/x → 5x = 30 → x = 6
3. C) 6 in - Better to revise this one.
4. C) 50
1 in = 20 mi → 2.5 in = 2.5 × 20 = 50 miles
5. E) 20
6/8 = 15/x → 6x = 120 → x = 20
6. C) 1 in = 4 ft
3 in = 12 ft → 1 in = 4 ft
7. D) 9
Proportion: 12/6 = 18/x → 12x = 108 → x = 9
8. D) 21
5:15 = 7:x → 5x = 105 → x = 21
9. C) 1 in = 8 ft
10 in = 80 ft → 1 in = 8 ft
10. C) 1 in = 5 ft
30 in = 150 ft → 1 in = 5 ft
11. C) 10 cm
5:12 = x:24 → 12x = 120 → x = 10
12. C) 5 in
3 in = 60 mi → 1 in = 20 mi → 100/20 = 5 in
13. C) 30
Scale factor = 2 → 15 × 2 = 30
14. D) 84 in
7 × 12 = 84 in
15. B) 24
36:48 = 18:x → 36x = 864 → x = 24
16. C) 20 ft
5 in × 4 = 20 ft
17. C) 12
9:6 = 18:x → 9x = 108 → x = 12
18. C) 1 in = 8 ft
8 in = 64 ft → 1 in = 8 ft
19. D) 72 in
6 in × 12 = 72 in
20. A) 12 cm
60 ÷ 5 = 12 cm
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