** Definition of Scale Factor**

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

**More about Scale Factor**

- A scale factor is a number used as a multiplier in scaling.
- A scale factor is used to scale shapes in 1, 2, or 3 dimensions.
- Scale factor can be found in the following scenarios:

1.**Size Transformation:**In size transformation, the scale factor is the ratio of expressing the amount of magnification.

2.**Scale Drawing:**In scale drawing, the scale factor is the ratio of measurement of the drawing compared to the measurement of the original figure.

3.**Comparing Two Similar Geometric Figures:**The scale factor when comparing two similar geometric figures, is the ratio of lengths of the corresponding sides.

**Example of Scale Factor**

- ABCD and PQRS are similar polygons. Then the scale factor of polygon ABCD to polygon PQRS is the ratio of the lengths of the corresponding sides.

Scale factor = BC:QR = 3:8.

**Solved Example on Scale Factor**

Find the scale factor from the larger rectangle to the smaller rectangle, if the two rectangles are similar.

Choices:

A. 5:1

B. 5:6

C. 6:5

D. 6:7

Correct Answer: B

Solution:

Step 1:If we multiply the length of one side of the larger rectangle by the scale factor we get the length of the corresponding side of the smaller rectangle.

Step 2:Dimension of larger rectangle × scale factor = dimension of smaller rectangle

Step 3:24 × scale factor = 20 [Substitute the values.]

Step 4:Scale factor = 20/24 [Divide each side by 24.]

Step 5:Scale factor = = 5:6 [Simplify.]

Therefore, scale factor from the larger rectangle to the smaller rectangle is 5:6.

**Related terms for Scale Factor**

- Dimension
- Length
- Multiplier