#### Solved Examples and Worksheet for Scale Drawings, Maps, and Indirect Measurement

Q1A child saw a tall building of height 2000 ft with binoculars and was surprised to see it as 20 in. in his binoculars. What scale in the binoculars could give such projection?

A. 1120
B. 112
C. 112000
D. 11200

Step: 1
1 ft = 12 in.
Step: 2
The height of building in inches
12 x 2000 = 24000 in.
[Conversion of feet to inches.]
Step: 3
The scale used by binoculars = The image height of building / The actual height of building
2024000 = 11200
[Finding the scale used in binoculars.]
Step: 4
The scale used by the binoculars is 11200.
Q2A cardboard model of a Honda bike is part of an outdoor display. Its height is 4 ft. The actual Honda bike is 5 ft long and 2 ft high. Find the length of the model, if its dimensions are proportionate to the real bike.

A. 12 ft
B. 11 ft
C. 9 ft
D. 10 ft

Step: 1
Let n be the length of Honda bike cardboard model.
Step: 2
25 = 4n
[Write a proportion.]
Step: 3
n x 2 = 4 x 5
[Write the cross products.]
Step: 4
n = 10
[Simplify the expression.]
Step: 5
The length of the Honda bike cardboard model is 10 ft.
Correct Answer is :   10 ft
Q3An automobile has drawn the design model of a car on paper using a scale of 1:9. The length of the car on the paper was 14 in. What is the actual length of the car?

A. 252 in.
B. 63 in.
C. 126 in.
D. None of the above

Step: 1
Let x be the actual length of the car.
Step: 2
14x = 19
[Use scale transformation to represent the actual length of the car.]
Step: 3
x = 14 × 9 = 126 in.
[Simplify.]
Step: 4
The actual length of the car is 126 in.
Correct Answer is :   126 in.
Q4A square of side 3 cm is enlarged to have a side of 9 cm. Find the scale factor.

A. 4
B. 5
C. 3
D. 6

Step: 1
Scale factor = (length of enlarged square side) / (length of original square side)
Step: 2
= 93
[Substitute the values.]
Step: 3
= 9÷33÷3 = 31 = 3
[Divide numerator and denominator by their GCF, 3 and simplify.]
Step: 4
The scale factor is 3.
Q5Harry potter is 4 feet 4 inches tall in the cinema and a toy of Harry Potter measures 1 foot 1 inch. Find the scale factor the toy company uses.

A. 1/3
B. 1/4
C. 1/2
D. None of the above

Step: 1
As,1 feet = 12 inches, the actual height of Harry potter = 4 feet 4 inches = (4 x 12) + 4 inches = 52 inches
[Convert feet to inches.]
Step: 2
The height of toy of Harry potter = 1 feet 1 inch = (1 x 12) + 1 = 13 inches.
Step: 3
Scale = the height of toy of Harry potter/the actual height of Harry potter = 1352 = 14
Step: 4
The scale factor used is 14.
Q6The actual length of a film is 0.9 inches and the length, after projecting it on to the screen, is 3 inches. Find the scale factor of the projector.

A. 4.3
B. 4.6
C. 3.8
D. 3.3

Step: 1
Scale factor = (length after projection) / (actual length)
Step: 2
= 30.9 = 3.3
[Substitute the values and simplify.]
Step: 3
The scale factor of the projector is 3.3.
Q7A company wants to prepare a die casting model of a car. The actual length of the car is 4.5 m and the length of the model is 200 cm. Find the scale the company uses.

A. 1330
B. 12
C. 49
D. 715

Step: 1
1m = 100 cm, 4.5 m = 4.5 x 100 = 450 cm.
Step: 2
The scale = the length of the model/the actual length of the car = 200cm450cm = 49
Step: 3
The scale used to make the model is 49 .
Q8Dennis is examining a cell of size 0.04 in. through a microscope. The size of the cell when examined through the microscope is 1.2 in. Find the scale factor.
A. 140
B. 30
C. 130
D. 40

Step: 1
Scale factor = (size of the cell through the microscope) / (actual size of the cell)
= 1.20.04
[Substitute the values.]
Step: 2
= 1204
[Multiply and divide by 100 to remove the decimal in the denominator.]
Step: 3
= 30
[Divide.]
Step: 4
The scale factor is 30.
Q9A photographer reduced the length of a photograph from 2.5 ft to 0.5 ft. Find the scale factor he used.

A. 14
B. 5
C. 15
D. 4

Step: 1
Scale factor = (reduced length of the photograph) / (actual length of the photograph)
= 0.52.5 = 15
[Substitute the values and simplify.]
Step: 2
The scale factor is 15.
Q10The height of the Grad school logo is 12 in. The administration of the school is planning to enlarge the logo so that the height of the logo should be 15 in. Find the scale factor.
A. 2.25
B. 1
C. 1.75
D. 1.25

Step: 1
Scale factor = (height of the enlarged logo) / (actual height of the logo)
= 1512 = 54 = 1.25
[Simplify.]
Step: 2
The scale factor is 1.25.
Q11A graphic designer designed a logo according to a company's specifications. The length of the logo was 20 inches. When the company wanted him to reduce the size of the logo, he used a scale factor of 14 to reduce the size. Find the new length of the logo.

A. 8 inches
B. 7 inches
C. 6 inches
D. 5 inches

Step: 1
New length = (actual length of the logo) x (scale factor)
= 20 x 14 = 5 inches
[Substitute the values and simplify.]
Step: 2
The new length of the logo is 5 inches.
Correct Answer is :   5 inches
Q12A logo for a company uniform was designed on a paper and it measured 17.5 inches in length. The designer was asked to decrease the size of the logo so that the logo on the uniform would measure 3.5 inches. Find the scale factor.

A. 16
B. 5
C. 15
D. 6

Step: 1
Scale factor = (length of the logo after reduction) / (actual length of the logo)
= 3.517.5 = 15
[Substitute the values and simplify.]
Step: 2
The scale factor is 15.
Q13A toy company wants to make a doll of Lady Diana, who was about 6 ft tall. The height of the doll is 2.4 feet. Find the scale factor.

A. 1225
B. 1730
C. 25
D. 1235

Step: 1
Scale factor = (height of the toy) / (actual height)
= 2.46 = 25
[Substitute the values and simplify.]
Step: 2
The scale factor is 25.
Q14Jim 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

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
Q15The height of a statue in a model was 6 inches. What is the original height of the statue, if the scale of the model was 1 inch : 75 meters?
A. 440 meters
B. 460 meters
C. 450 meters
D. 470 meters

Step: 1
Let, n be the actual height of the statue.
Step: 2
175 = 6n
[Write a proportion.]
Step: 3
n x 1 = 75 x 6
[Write a cross product.]
Step: 4
n = 450
[Multiply.]
Step: 5
So, the height of the statue in reality is 450 meters.
Correct Answer is :   450 meters