# Maps and Scale Drawings

## Lesson Preview

### What You'll Learn

1. To use proportions to solve problems involving scale

### … And Why

To 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.

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.

Making Models

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#### Real-World Problem Solving

GeographyFind the actual distance from Charlotte to Winston-Salem.

1. Use a centimeter ruler to find the map distance from Charlotte to Winston-Salem. The map distance is about 1.6 cm.
2. 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.

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