Solve Scale Drawing Problems

The scale in a scale drawing is often shown as a ratio.

A ratio of 1:100 means that 1 cm on the drawing represents 100 cm in actual real life.

This could also be written as 1 cm:1 m or 1 cm to 1 m.

We can put ratios into the same units by converting between them.

There are 100 cm in a metre.

This means that a scale of 1 cm to 5 m could also be written as 1:500

Example 1

Betty makes a scale drawing of her classroom.

She uses a scale of 1 cm to 2 m.

The actual length of her classroom is 10 m.

How long should she make her classroom, in cm, on her drawing?

Answer

The ratio is 1 cm to 2 m.

Every 2 m in real life is shown as 1 cm on the drawing.

10 m is 5 × 2 m.

On the drawing, this should be 5 cm.

You can check this:

1 cm: 2 m

We multiplied the 2 m by 5 to get to 10 m, so we need to do the same thing to the other side of the ratio.

1 x 5: 2 x 5

5:10

The drawing should be 5 cm.

Example 2

Charlie makes a scale drawing of the school hall.

The actual length of the hall is 25 m.

On his drawing, he makes the hall 5 cm long.

What scale is Charlie using?

Answer

The ratio is 5 cm to 25 m.

This simplifies like a fraction by dividing both numbers by 5.

So the ratio is 1 cm to 5 m.

This is 1 cm to 500 cm or 1:500

Let's have a go at some questions now.