scale factor


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