Computing Actual Lengths from a Scale Drawing

Examples, videos, and solutions to help Grade 7 students when given a scale drawing, compute the lengths in the actual picture using the scale factor.

New York State Common Core Math Grade 7, Module 4, Lesson 14

Worksheets for Grade 7

Lesson 14 Student Outcomes

• Given a scale drawing, students compute the lengths in the actual picture using the scale factor.

Lesson 14 Classwork

Example 1
The distance around the entire small boat is units 28.4. The larger figure is a scale drawing of the smaller drawing of the boat. State the scale factor as a percent, and then use the scale factor to find the distance around the scale drawing.

Exercise 1
The length of the longer path is 32.4 units. The shorter path is a scale drawing of the longer path. Find the length of the shorter path and explain how you arrived at your answer.

Example 2
Sherry designed her garden as shown in the diagram above. The distance between any two consecutive vertical grid lines is 1 foot, and the distance between any two consecutive horizontal grid lines is also 1 foot. Therefore, each grid square has an area of one square foot. After designing the garden, Sherry decides to actually build the garden 75% of the size represented in the diagram.
a. What are the outside dimensions shown in the blueprint?
b. What will the overall dimensions be in the actual garden? Write an equation to find the dimensions. How does the problem relate to the scale factor?
c. If Sherry plans to use a wire fence to divide each section of the garden, how much fence does she need?
d. If the fence costs $3.25 per foot plus 7% sales tax, how much would the fence cost in total?

Exercise 2
Race Car #2 is a scale drawing of Race Car #1. The measurement from the front of Car #1 to the back of Car #1 is 12 feet, while the measurement from the front of Car #2 to the back of Car #2 is 39 feet. If the height of Car #1 is 4 feet, find the scale factor, and write an equation to find the height of Car #2. Explain what each part of the equation represents in the situation.

Exercise 3
Determine the scale factor and write an equation that relates the vertical heights of each drawing to the scale factor. Explain how the equation illustrates the relationship.

Exercise 4
The length of a rectangular picture is 8 inches, and the picture is to be reduced to be 45 1/2% of the original picture. Write an equation that relates the lengths of each picture. Explain how the equation illustrates the relationship.

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