Lesson 10
Changing Scales in Scale Drawings
Problem 1
Here is a scale drawing of a swimming pool where 1 cm represents 1 m.
![A scale drawing of a rectangular swimming pool.](https://cms-im.s3.amazonaws.com/ktYRX1Kd3BiodzHuF9mkZuhW?response-content-disposition=inline%3B%20filename%3D%227-7.1.10.SwimmingPool.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.10.SwimmingPool.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=20240727T002957Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1f7f16a1607115ae3ba67374ecf2ac63b7485291d221a5a2a91a561ee0b2d8aa)
- How long and how wide is the actual swimming pool?
- Will a scale drawing where 1 cm represents 2 m be larger or smaller than this drawing?
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Make a scale drawing of the swimming pool where 1 cm represents 2 m.
Solution
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Problem 2
A map of a park has a scale of 1 inch to 1,000 feet. Another map of the same park has a scale of 1 inch to 500 feet. Which map is larger? Explain or show your reasoning.
Solution
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Problem 3
On a map with a scale of 1 inch to 12 feet, the area of a restaurant is 60 in2. Han says that the actual area of the restaurant is 720 ft2. Do you agree or disagree? Explain your reasoning.
Solution
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Problem 4
If Quadrilateral Q is a scaled copy of Quadrilateral P created with a scale factor of 3, what is the perimeter of Q?
![Trapezoid P. Base 1 = 7 units, base 2= 25 units. Left and right sides = 15 units.](https://cms-im.s3.amazonaws.com/Ni7jTxfUJcya7sqyvtLk8TR1?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.36.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.36.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=20240727T002957Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ab33adefa9b54c0242c1aa22b45198fd4ed66597d3d40a107d3875d1a13d4222)
Solution
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(From Unit 1, Lesson 3.)Problem 5
Triangle \(DEF\) is a scaled copy of triangle \(ABC\). For each of the following parts of triangle \(ABC\), identify the corresponding part of triangle \(DEF\).
- angle \(ABC\)
- angle \(BCA\)
- segment \(AC\)
- segment \(BA\)
![Two triangles labeled ABC and DEF.](https://cms-im.s3.amazonaws.com/T2yrTYGGmgcZaLHovPqbjsAc?response-content-disposition=inline%3B%20filename%3D%227-7.1.PP.New.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.PP.New.Image.04.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=20240727T002957Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=122947c8c983e8719a38290713ade65c4f7f465ff439b60bcaa16283698e66cc)
Solution
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(From Unit 1, Lesson 2.)