Scale drawings and scale factors

A **scale drawing** is a drawing of a real object in which all the dimensions are proportional to the real object. A scale drawing can be larger or smaller than the object it represents. The scale is the ratio of the drawing size to the actual size of the object.

- The ratio of the length of the scale drawing to the corresponding length of the actual object is called as
**scale factor**.
- The ratio of any two corresponding lengths in two similar geometric figures is called as
**scale factor**.

**On a map having a scale of 1 inch = 25 miles, the distance between two cities is 3.2 inches. What is the actual distance between the two cities?**

Let *d* = the actual distance between the cities. Write and solve a proportion. Use the scale written as a fraction.

1 × *d* = 25 × 3.2 Cross products

* d* = 80 Simplify.

The actual distance between the two cities is 80 miles.

**Designers are creating a child-sized version of a doll’s dress. If they use a scale of 10 inches = 1 inch and the doll’s dress has a length of 4.5 inches, what is the length of the child-sized dress?**

Write a proportion using the scale.

10 × 4.5 = 1 × *c* Find the cross products.

45 = *c* Multiply.

The child-sized dress is 45 inches long.

A pond is being dug according to plans that have a scale of 4 inch = 80 feet. The maximum distance across the pond is 11 inches on the plans. What will be the actual maximum distance across the pond?

The maximum distance across the pond will be feet