Scale drawings: word problems

Key notes:-

1. Introduction to Scale Drawings

  • A scale drawing is a proportional representation of an object or area.
  • The scale expresses the ratio between the dimensions in the drawing and the actual dimensions (e.g., 1 cm:10 m).
  • Used in maps, blueprints, and models to depict large objects or areas in manageable sizes.

2. Key Terms

  • Scale factor: The ratio used to scale dimensions up or down.
  • Actual size: The real-life dimensions of the object.
  • Scaled size: The dimensions as represented in the drawing.
  • Proportionality: Ensuring all dimensions maintain the same ratio.

3. Understanding the Scale

  • Example: A scale of 1:50 means 1 unit in the drawing equals 50 units in real life.
  • Units must match (e.g., cm to cm, m to m).

4. Solving Word Problems

  • Step 1: Identify the scale provided.
  • Step 2: Write the proportion between the scaled and actual dimensions.
  • Step 3: Solve for the missing value using cross-multiplication.
  • Step 4: Verify that units are consistent throughout the calculation.

Learn with an example

🔔 Ayana measured a swimming pool and made a scale drawing. The scale she used was 7 centimetres : 3 metres. The pool is 28 centimetres in the drawing. How wide is the actual pool?

Write the scale of the drawing as a fraction:

7cm /3m

Write an equivalent fraction with 28 centimetres as the numerator.

7cm × 4 /3m × 4 =28 cm / 12 m

The actual pool is 12 metres wide.

🔔 Pablo wants to check out a book from his local library, but it is not available. Pablo decides to visit the library in Wildgrove to see if that location has a copy of the book. On a map, the two libraries are 48 centimetres apart. If the scale of the map is 1 centimetre : 1 kilometre, then what is the actual distance between the two libraries?

Write a ratio that represents the scale of the map in centimetres to
kilometres: 1/1.

Write a ratio that relates the centimetres between the two libraries on the
map to the kilometres between the two libraries in real life: 48/d.

Use those ratios to set up a proportion and solve.

1/1 = 48/d

Multiply both sides by d.

1/1 xd = 48/d xd

Simplify
d = 48
The actual distance between the two libraries is 48 kilometres.


.

🔔 On a public transportation map, two stations are 7 centimetres apart, whereas in real life the distance between them is 7 kilometres. What scale does the map use?

1 centimetre = _______ kilometres

Write a ratio that relates the centimetres between the two stations on the map to the

kilometres between the two stations in real life: 7/7 ,

To find the scale of the map, rewrite this ratio with 1 in the numerator.

7/7 = 1/1 Divide the numerator and denominator by 7

The map uses a scale of 1 centimetre = 1 kilometre.

Let’s Practice!