#### Solved Examples and Worksheet for Application Problems involving Scale Drawings

Q1Length of a lake is 5 inches on map. The map of the lake has a scale of 1 inch : 20 miles. Find the actual length of the lake.
A. 150 miles
B. 50 miles
C. 80 miles
D. 100 miles

Step: 1
Let k be the actual length of the lake.
Step: 2
120 = 5k
[Write the proportion.]
Step: 3
k x 1 = 5 x 20
[Write the cross products.]
Step: 4
k = 100
[Multiply.]
Step: 5
The actual length of the lake is 100 miles.
Correct Answer is :   100 miles
Q2A bridge was supposed to be built across a river and the architect drew a 3 cm long bridge using a scale 1 cm : 3 miles on paper. Find the actual length of the bridge.
A. 11 miles
B. 10 miles
C. 12 miles
D. 9 miles

Step: 1
Let b be the length of the bridge.
Step: 2
13 = 3b
[Write the proportion using the scale.]
Step: 3
b x 1 = 3 x 3
[Write the cross products.]
Step: 4
b = 9
[Multiply.]
Step: 5
The length of the bridge is 9 miles.
Correct Answer is :   9 miles
Q3A Botany student drew a sketch of a plant, using a scale of 1 inch : 3.3 ft. Find the actual height of the plant, if the sketch is 2 in. long.
A. 5.6 feet
B. 6.3 feet
C. 6.6 feet
D. 7.6 feet

Step: 1
Let n be the actual height of the plant.
Step: 2
13.3 = 2n
[Write the proportion using the scale.]
Step: 3
n x 1 = 2 x 3.3
[Write the cross products.]
Step: 4
n = 6.6
[Multiply.]
Step: 5
The actual height of the plant is 6.6 feet.
Correct Answer is :   6.6 feet
Q4A model baseball bat was placed at the entrance of a stadium, which measured 13 feet in length. A scale of 1 foot : 2 inches is used for the model. Find the actual length of the bat.

A. 27 inches
B. 26 inches
C. 29 inches
D. 25 inches

Step: 1
Let n be the actual length of the bat.
Step: 2
12 = 13n
[Write the proportion.]
Step: 3
n × 1 = 2 × 13
[Write the cross products.]
Step: 4
n = 26
[Simplify.]
Step: 5
The actual length of the bat is 26 inches.
Correct Answer is :   26 inches
Q5An 105 ft tall statue was carved and the sculptor used a 15 in. sketch of the statue as a blueprint. What scale did the sculptor use?

A. 1 in. : 1 ft
B. 1 in. : 7 ft
C. 3 in. : 7 ft
D. 2 in. : 6 ft

Step: 1
The scale is the ratio of size of the statue in the blue print to the size of the original statue.
Step: 2
15105
[Write the ratio.]
Step: 3
= 15÷15105÷15 = 17
[Divide both numerator and denominator by the GCF 15.]
Step: 4
The scale used by the sculptor is 1 in. : 7 ft.
Correct Answer is :   1 in. : 7 ft
Q6The height of a tree in a picture was 2 in. Find the actual height of the tree, if the scale of the picture was 1in : 9 m.
A. 18 meters
B. 20 meters
C. 16 meters
D. 9 meters

Step: 1
Let n be the actual height of the tree.
Step: 2
1in.9m = 2in.n
[Write the scale and its related Proportion.]
Step: 3
n x 1 = 2 x 9
[Write the cross products.]
Step: 4
n = 18
[Multiply.]
Step: 5
So, the actual height of the tree is 18 meters.
Correct Answer is :   18 meters
Q7An artist drew a sketch of Westminster Abbey in London and it measured 100 cm. Find the scale used by him, if the chapel measures 40 meters.

A. 2 cm : 0.40 m
B. 1 cm : 1.40 m
C. 1 cm : 0.40 m
D. 1 cm : 0.50 m

Step: 1
The scale is the ratio of the length of sketch to the length of the Chapel.
Step: 2
10040 = (100÷100)(40÷100) = 1 cm : 0.40 m
[Divide both numerator and denominator by 100.]
Step: 3
The artist used a scale of 1 cm : 0.40 m.
Correct Answer is :   1 cm : 0.40 m
Q8A map is drawn to a scale, such that a distance of 1 inch on the map represents a distance of 80 miles. What is the distance between the two cities, Rupert and Rushville, if the distance between them is 6.3 inches on the map?
A. 504 miles
B. 560 miles
C. 400 miles
D. 480 miles

Step: 1
Let m be the distance between the two cities (in miles).
Step: 2
180 = 6.3m
[Write a proportion.]
Step: 3
1 × m = 80 × 6.3
[Write the cross products.]
Step: 4
m = 504
[Multiply.]
Step: 5
The distance between Rupert and Rushville is 504 miles.
Correct Answer is :   504 miles
Q9Mike drew a sketch of a tree using a scale of 14 inch : 1 meter. Find the height of the tree, if it measures 2 inches in the sketch.

A. 8 meters
B. 4 meters
C. 2 meters
D. 16 meters

Step: 1
Let n be the actual height of the tree.
Step: 2
2n= 141
[Write the proportion.]
Step: 3
n × 1 = 2 × 4
[Write the cross products.]
Step: 4
n = 8
[Simplify.]
Step: 5
The actual height of the tree is 8 meters.
Correct Answer is :   8 meters
Q10A student drew a sketch of a coconut tree using a scale of 1 cm = 2m. Find the actual height of the tree, if it measures 2 cm in the sketch.

A. 3 m
B. 5 m
C. 4 m
D. 2 m

Step: 1
The scale is 1 cm is equal to 2 m
Step: 2
1 cm on the map represents 2 m on the ground.
Step: 3
So, 2 cm on the map = 2 × 2 m = 4 m
Step: 4
Therefore, the actual height of the coconut tree is 4 m
Correct Answer is :   4 m