Scale drawings: word problems

Key Notes :

Definition of Scale Drawings

  • A scale drawing is a proportional representation of an object or place.
  • It is used in maps, blueprints, and models.

Understanding Scale

  • The scale shows the ratio between the drawing’s measurements and the actual object.
  • Example: A scale of 1 cm : 5 m means 1 cm on the drawing represents 5 meters in real life.

Types of Scale

  • Enlargement: When the scale factor is greater than 1.
  • Reduction: When the scale factor is less than 1.
  • Same Size: When the scale is 1:1 (actual size).

Solving Word Problems

  • Step 1: Identify the given scale.
  • Step 2: Find the actual or scaled measurement using multiplication or division.
  • Step 3: Check units and convert if needed.

Common Types of Word Problems

  • Finding Actual Measurements: Given a scale drawing, determine the real-life size.
  • Finding Drawing Measurements: Given actual measurements, determine the scaled size.
  • Comparing Scale Drawings: Identify which drawing is more accurate.

Examples

  • A map uses a scale of 1 cm : 10 km. If two cities are 3 cm apart on the map, the real distance is:

3 × 10 = 30 km

  • A blueprint of a room uses a scale of 1 inch : 4 feet. If the room is 12 feet long, its blueprint length is:

12 ÷ 4 = 3 inches12

Learn with an example

👉Tony made a scale drawing of a swimming pool. The pool, which is 18 metres wide in real life, is 2 millimetres wide in the drawing.

What is the scale of the drawing?

1 millimetre : _____ metres

Write the ratio of the width of the pool in the drawing to the width of the actual pool. Write the ratio in fraction form.

2 mm / 18 m

Simplify the fraction.

2 mm ÷ 2 / 18 m ÷ 2 = 1 mm / 9 m

The scale of the drawing is 1 millimetre : 9 metres.

👉 Eva measured a summer camp and made a scale drawing. She used the scale 1 millimetre : 3 metres. If the sand volleyball court is 3 millimetres in the drawing .

How wide is the actual volleyball court?

 _____ metres

Write the scale of the drawing as a fraction:

1 mm / 3 m

Write an equivalent fraction with 3 millimetres as the numerator.

1 mm × 3 / 3 m × 3 = 3 mm / 9 m

The actual volleyball court is 9 metres wide.

👉 Mitchell drew a scale drawing of a house and its lot. In real life, the front patio is 30 metres long. It is 3 centimetres long in the drawing.

What scale did Mitchell use for the drawing?

1 centimetre : _______ metres

Write the ratio of the length of the patio in the drawing to the length of the actual patio. Write the ratio in fraction form.

3 cm / 13 m

Simplify the fraction.

3 cm ÷ 3 / 30 m ÷ 3 = 1 cm / 10 m

The scale of the drawing is 1 centimetre : 10 metres.

let’s practice! 🖊️