Lesson 5: Scale Drawings

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

The scale factor is the ratio of the lengths in the new figure to the corresponding lengths in the original figure.

Examples

• A map has a scale factor of $\frac{1}{10000}$. A road that is 3 cm long on the map is $3 \times 10000 = 30000$ cm, or 300 meters, in real life.
• A triangle with a base of 8 inches is enlarged to a similar triangle with a base of 20 inches. The scale factor is $\frac{20}{8} = 2.5$.
• To reduce a 12-foot wall to fit on a blueprint with a scale factor of $\frac{1}{48}$, its length on the blueprint is $12 \times \frac{1}{48} = \frac{1}{4}$ foot, or 3 inches.

Explanation

The scale factor is the number you multiply by to change the size of a figure. A scale factor greater than 1 makes the figure bigger (an enlargement), while a factor between 0 and 1 makes it smaller (a reduction).

Property

To solve problems with scale drawings, set up a proportion where the ratio of the drawing measurement to the actual measurement is constant.

• To find an actual distance: multiply or divide using the scale ratio.
• To find a drawing length: divide the actual length by the scale's rate.

Examples

• Finding Actual Distance: A map scale says 1 inch = 5 miles. If the distance between two cities on the map is 4 inches, the actual distance is 4 x 5 = 20 miles.
• Finding Drawing Length: A blueprint uses a scale of 1 inch = 4 feet. A room's actual width is 14 feet. The width on the blueprint is 14 / 4 = 3.5 inches.

Explanation

A scale provides the ratio between the measurements on a drawing and the measurements in real life. By keeping drawing measurements grouped together and actual measurements grouped together, you can use basic multiplication or division to solve for any unknown distance.