Solved Examples and Worksheet for Scale Drawings using Ratios and Proportions

Q1A museum displayed a model of a fighter plane. The length of the model is 29 cm and the scale used to make the model was 1 cm to represent 1.2 ft. What would be the actual length of the plane?
A. 24.17 ft
B. 30.2 ft
C. 34.8 ft
D. 31.2 ft

Solutions
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Step: 1
Let n be the actual length of the plane.
Step: 2
11.2 = 29n
  [Write the scale and its related proportion.]
Step: 3
n × 1 = 1.2 × 29
  [Write the cross products.]
Step: 4
n = 34.8
  [Simplify.]
Step: 5
The actual length of the plane is 34.8 ft.
Correct Answer is :   34.8 ft
Q2Jim has drawn a picture of the Eiffel Tower using a scale 1 inch : 82 yd as shown. Find the actual height of the Eiffel Tower.


A. 322 yd
B. 324 yd
C. 326 yd
D. 328 yd

Solutions
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Step: 1
Let n be the height of the actual Eiffel Tower.
Step: 2
182 = 4n
  [Write the scale and its related proportion.]
Step: 3
n × 1 = 82 × 4
  [Write the cross products.]
Step: 4
n = 328
  [Multiply.]
Step: 5
The actual height of the Eiffel Tower is 328 yd.
Correct Answer is :   328 yd
Q3The architect, who designed the plan for hospital building was told that the height of the hospital building should not exceed 247 feet. The architect designed the building on paper using a scale 2 inch : 19 feet. What should be the height of the building on paper?

A. 27 in.
B. 25 in.
C. 28 in.
D. 26 in.

Solutions
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Step: 1
Let n be the height of the building on paper.
Step: 2
219 = n247
  [Write the scale and its related proportion.]
Step: 3
n x 19 = 247 x 2
  [Write the cross products.]
Step: 4
n = 26
  [Divide both sides by 19 and then simplify.]
Step: 5
The height of the building on paper is 26 in..
Correct Answer is :   26 in.
Q4An oil company looked for a feasible area on map for constructing a gas station. The length of the land spotted by them on the map is 9 inches. The scale of the map is 1 inch : 4 ft. What would be the actual length of the land?

A. 38 ft
B. 36 ft
C. 35 ft
D. 37 ft

Solutions
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Step: 1
Let n be the actual length of the land.
Step: 2
14 = 9n
  [Write the scale and its related proportion.]
Step: 3
n x 1 = 4 x 9
  [Write the cross products.]
Step: 4
n = 36
  [Simplify.]
Step: 5
The actual length of the land is 36 ft.
Correct Answer is :   36 ft
Q5The scale of a soccer ground map is 1 cm : 11 yd and the length of the original ground is 110 yd. What is the length of the soccer ground on the map?

A. 10 cm
B. 13 cm
C. 12 cm
D. 8 cm

Solutions
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Step: 1
Let n be the length of the soccer ground on map.
Step: 2
111 = n110
  [Write the scale and its related proportion.]
Step: 3
n × 11 = 1 × 110
  [Write the cross products.]
Step: 4
n = 10
  [Simplify.]
Step: 5
The length of the soccer ground on the map is 10 cm.
Correct Answer is :   10 cm
Q6A student was shown a map of a region he lived in and was informed that 1 in.2 on the map measures 10 mi2 on land. If a region measures 4 in.2 on the map, then find the area of the actual region.

A. 39 mi2
B. 40 mi2
C. 41 mi2
D. None of the above

Solutions
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Step: 1
Let n represent the actual area of the region.
Step: 2
110 = 4n
  [Write the scale and its related proportion.]
Step: 3
n x 1 = 10 x 4
  [Write the cross products.]
Step: 4
n = 40
  [Simplify.]
Step: 5
The actual area of the region is 40 mi2.
Correct Answer is :   40 mi2
Q7Victor saw a photograph of an antenna and it measured 6 meter in length. What would be the actual length of the antenna, if the scale is 0.3 meter : 4 meter?

A. 79 meters
B. 80 meters
C. 81 meters
D. None of the above

Solutions
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Step: 1
Let n be the actual length of the antenna.
Step: 2
0.34 = 6n
  [Write the scale and its related proportion.]
Step: 3
n x 0.3 = 6 x 4
  [Write the cross products.]
Step: 4
n = 80
  [Simplify.]
Step: 5
Hence, the actual length of the antenna is 80 meters.
Correct Answer is :   80 meters
Q8An 8th grade student is writing an online assignment. As the font of the text is not clear, he increased the font size representing a scale 1 inch : 2 inch. Find the size of the font, if the original size of the text before being changed was 0.25 in.

A. 0.5 in.
B. 2.5 in.
C. 1.5 in.
D. None of the above

Solutions
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Step: 1
Let the size of the font be n.
Step: 2
12 = 0.25n
  [Write the scale and its related proportion.]
Step: 3
n x 1 = 2 x 0.25
  [Write the cross products.]
Step: 4
n = 0.5 in.
  [Simplify.]
Step: 5
The size of changed font is 0.5 in.
Correct Answer is :   0.5 in.
Q9A Pen manufacturing company wants to introduce a model of their pen. The scale of the model they want to make is 4 cm: 5 feet. If the height of the actual pen is 12 cm, then what would be the height of the model?
A. 14 feet
B. 15 feet
C. 16 feet
D. None of the above

Solutions
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Step: 1
Let n be the height of the model.
Step: 2
45 = 12n
  [Write the scale and its related proportion.]
Step: 3
n x 4 = 5 x 12
  [Write the cross products.]
Step: 4
n = 15
  [Simplify.]
Step: 5
The height of the model is 15 feet.
Correct Answer is :   15 feet
Q10The height of an elephant in the picture is 10 in. The scale of the picture is 5 in. : 7 ft. What would be the actual height of the elephant?

A. 16 ft
B. 14 ft
C. 15 ft
D. 13 ft

Solutions
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Step: 1
Let n be the actual height of the elephant.
Step: 2
57 = 10n
  [Write the scale and its related proportion.]
Step: 3
n x 5 = 10 x 7
  [Write the cross products.]
Step: 4
n = 14
  [Simplify.]
Step: 5
The height of the actual elephant is 14 ft.
Correct Answer is :   14 ft
Q11An artist drew a painting on a postcard of length 5 in. He used a scale of 3 in. : 8 in. Find the length of the original painting.
A. 13.3 in.
B. 15.3 in.
C. 14.3 in.
D. 12.3 in.

Solutions
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Step: 1
Let n be the actual height of the painting.
Step: 2
38 = 5n
  [Write the scale and its related proportion.]
Step: 3
n x 3 = 5 x 8
  [Write the cross products.]
Step: 4
n = 13.3
  [Simplify.]
Step: 5
The length of the actual painting is 13.3 in.
  [Simplify.]
Correct Answer is :   13.3 in.
Q12An architect was asked to design a blueprint of a commercial complex of height 184 feet. The architect uses a scale of 3 inch: 46 feet. Find the height of the building in his blueprint.
A. 13 inches
B. 12 inches
C. 11 inches
D. None of the above

Solutions
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Step: 1
Let n be the height of the building in the blueprint.
Step: 2
346 = n184
  [Write the scale and its related proportion.]
Step: 3
n x 46 = 3 x 184
  [Write the cross products.]
Step: 4
n = 12
  [Simplify.]
Step: 5
The height of the commercial complex in the blueprint will be 12 inches.
Correct Answer is :   12 inches

HighSchool Math