# Maps and Scale Drawings

## Lesson Preview

## What You'll Learn- To use proportions to solve problems involving scale
## … And WhyTo use maps, as in Example 2 |

## Solving Problems Involving Scale

A scale drawing is an enlarged or reduced drawing of an object that is similar to an actual object. Maps and floor plans are smaller than the actual size. A scale drawing of a human cell is larger than the actual size.

##### Reading Math

On a map, the equal sign in 1 in. = 30 mi does not mean that the two quantities are equal, as it would in an equation.

A scale is the ratio that compares a length in a drawing to the corresponding length in the actual object. If a 30-mile road is 1 in. long on a map, you can write the scale of the map in these three ways:

#### Using a Scale Drawing

You have a scale drawing of a boat. The length of the boat on the drawing is 3 cm. What is the actual length of the boat?

Write the scale of the drawing, 1 cm = 1.5 m, as . Then write a proportion in which each ratio compares centimeters to meters.

Let *n* represent the actual length of the boat.

The actual length of the boat is 4.5 m.

You can use proportions and a map's scale to find actual distances.

#### Real-World Problem Solving

GeographyFind the actual distance from Charlotte to Winston-Salem.

- Use a centimeter ruler to find the map distance from Charlotte to Winston-Salem. The map distance is about 1.6 cm.
- Use a proportion to find the actual distance. Let
*n*represent the actual distance.

The actual distance from Charlotte to Winston-Salem is about 120 km.

You can use the GCF of two numbers to find the scale of a drawing or a model.

#### Finding the Scale

ModelsRefer to the model boxcar shown at the right. The actual length of a boxcar is 609 in. What is the scale of the model?

The scale is 1 in. : 87 in.

### Investigation:Making a Scale Drawing

Make a scale drawing of your classroom.

- Using a meter stick or yardstick, measure the classroom. Measure the length and width of the room and anything else you think you need.
- Choose a scale large enough to produce a good drawing, but small enough to fit on your paper.
- Complete your drawing. Include the scale.

Exercises Click here to view the Exercises for this lesson.

Investigation Click here to view the Investigation: Plan a Trip.