 # 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: d

#### 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. d

The actual length of the boat is 4.5 m. Check Understanding

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

##### Video Math Making Models

Play Video

8.6 MB

#### Real-World Problem Solving d

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. d

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

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. Check Understanding

### 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. Click here to view the Exercises for this lesson. Click here to view the Investigation: Plan a Trip.

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