Lesson 7

Units in Scale Drawings

Let’s explore a different way to express scales.

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.)

  1. 1 in to 1 ft

  2. 1 in to 1 m

  3. 1 in to 1 yd

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?

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

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

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. 


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:

  1. From T to S
  2. From S to R
  3. From R to T
  4. From T to R
(From Unit 2, Lesson 3.)