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 map is drawn using a scale of 2 inches : 20 meters. If the length of a pavel path on the map is 9 inches, then find the actual length of the pavel path

The actual length of the pavel path is meters