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.

Video Examples: Proportions, Triangles, MissingSides, Scale Factors


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

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

    example of  Scale Factor
    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= 5:6 [Simplify.]
    Therefore, scale factor from the larger rectangle to the smaller rectangle is 5:6.

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