Skill: Solve scale drawing problems

A scale tells you how a length in a drawing compares with the actual length. It is a multiplicative relationship, not an amount to add.

For example, suppose a floor plan uses the scale

$$1\text{ cm}=4\text{ m}.$$

This means every $1$ centimeter on the drawing represents $4$ meters in real life.

Example: A room is $6.5$ cm long on the floor plan. How long is the actual room?

1. Identify the scale and the drawing length.

$$1\text{ cm}\longrightarrow 4\text{ m}$$ $$6.5\text{ cm}\longrightarrow x\text{ m}$$

2. Set up a proportion. Match drawing lengths with actual lengths:

$$\frac{1\text{ cm}}{4\text{ m}}=\frac{6.5\text{ cm}}{x\text{ m}}$$

3. Solve by multiplying the drawing length by the scale factor.

   Since $1$ cm represents $4$ m,

$$x=6.5\times 4=26$$

4. State the answer with units.

   The actual room is

$$\boxed{26\text{ meters long}}.$$

Check: $6.5$ cm is $6.5$ groups of $1$ cm, so it represents $6.5$ groups of $4$ m, or $26$ m. Always keep the drawing and actual measurements matched correctly and use the units given by the scale.