Lesson 10

Changing Scales in Scale Drawings

Let’s explore different scale drawings of the same actual thing.

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.
  1. How long and how wide is the actual swimming pool? 
  2. Will a scale drawing where 1 cm represents 2 m be larger or smaller than this drawing?

  3. Make a scale drawing of the swimming pool where 1 cm represents 2 m.

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. 

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.

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.
(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. 
(From Unit 1, Lesson 2.)