Lesson 7
Units in Scale Drawings
Problem 1
A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. Explain your reasoning. (There are about 1.1 yards in a meter, and 2.54 cm in an inch.)
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1 in to 1 ft
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1 in to 1 m
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1 in to 1 yd
Solution
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Problem 2
Elena finds that the area of a house on a scale drawing is 25 square inches. The actual area of the house is 2,025 square feet. What is the scale of the drawing?
Solution
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Problem 3
Which scales are equivalent to 1 inch to 1 foot? Select all that apply.
1 to 12
\(\frac{1}{12}\text{ to }1\)
100 to 0.12
5 to 60
36 to 3
9 to 108
Solution
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Problem 4
Which of these scales are equivalent to 3 cm to 4 km? Select all that apply. Recall that 1 inch is 2.54 centimeters.
0.75 cm to 1 km
1 cm to 12 km
6 mm to 2 km
0.3 mm to 40 m
1 inch to 7.62 km
Solution
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Problem 5
These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle? Explain or show how you know.
![Scaled copies of two triangles. Triangle on left, height = 3. Triangle on right, height = 6.](https://cms-im.s3.amazonaws.com/oQEvgYx2GEX898MTHKMnK5re?response-content-disposition=inline%3B%20filename%3D%227.1.A.PP.Image.44%25282%2529.png%22%3B%20filename%2A%3DUTF-8%27%277.1.A.PP.Image.44%25282%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004526Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f610c11f5bede40839ba2746f07f965260ed1f6c1d69bc597dae2bebdaf0744)
Solution
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Problem 6
Figures R, S, and T are all scaled copies of one another. Figure S is a scaled copy of R using a scale factor of 3. Figure T is a scaled copy of S using a scale factor of 2. Find the scale factors for each of the following:
- From T to S
- From S to R
- From R to T
- From T to R
Solution
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(From Unit 2, Lesson 3.)