Lesson 1: Scale Drawings and Scale Factors

Property

A scale drawing shows an object in two dimensions with all parts in proportion to the real thing, while a scale model represents the same idea in three dimensions.
The scale is the ratio that relates the dimensions of the drawing or model to the actual dimensions of the object, written as:

Examples

• A blueprint of a house is a scale drawing. The scale might be $1 \text{ inch} : 5 \text{ feet}$.
• A toy car is a scale model of a real car. The scale might be $1:18$.
• A map is a scale drawing. The scale might be $1 \text{ cm} : 10 \text{ km}$.

Explanation

A scale drawing or model represents a real object with all its dimensions reduced or enlarged by the same factor. The scale tells you how the drawing's measurements relate to the object's actual measurements. For example, a scale of $1 \text{ inch} : 3 \text{ feet}$ means that every inch on the drawing represents three feet on the actual object. This allows for the creation of conveniently sized representations of very large or very small objects.

Property

To find an actual distance from a scale drawing, first measure the distance on the drawing with a ruler. Then, use the provided scale (e.g., 1 inch : 100 miles) to set up a proportion or multiply by the scale factor to convert the measured length into the actual distance.

Examples

• A map has a scale of 1 inch : 50 miles. The distance between two cities on the map is 3 inches. The actual distance is $3 \text{ inches} \times \frac{50 \text{ miles}}{1 \text{ inch}} = 150$ miles.

• A building plan uses a scale of 1 cm : 2 meters. A room is 5.5 cm long on the plan. Its actual length is $5.5 \text{ cm} \times \frac{2 \text{ meters}}{1 \text{ cm}} = 11$ meters.