Scale Factors using Ratio

## Scale Factors using Ratio

Scale Factors are used in to enlarge and diminish the size of similar objects. If a drawing is enlarged with a scale factor of 4, it means that all the equivalent measures are 4 times larger when compared to the original drawing.

A scale factor of 1 indicates that the two objects are the same size. A scale factor that is greater than 1 is an enlargement. A scale factor of less than 1 indicates that the second object is smaller.

A scale factor is obtained from a unit ratio: that is, when the number on one side of the ratio is equal to one. A ratio of 2:7 is equivalent to a scale factor of 3.5. Divide both sides by 2 for 1:3.5. The scale factor is the second number.

## Example 1

An equilateral triangle with sides is enlarged with a scale factor of 3. If the original triangle had sides of 4cm, what are the length of the sides on the enlarged triangle?

Multiply the original length by 3 for the larger length: 3 x 4cm = 12cm

## Example 2

A rectangle has a length of 4cm and a height of 2cm. A second rectangle has a length of 2cm and a height of 1cm. What is the scale factor of the second rectangle compared to the first?

Divide the second rectangle length by the first rectangle length

= 2 ÷ 4

= 0.5.

The second rectangle is smaller, so the scale factor will be less than 1.