Scaling Math Example 4

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Example 4

medium
A square has side length 55 cm. It is scaled by a factor of 33. By what factor does the area increase?

Solution

  1. 1
    New side length: 5×3=155 \times 3 = 15 cm.
  2. 2
    Original area: 52=255^2 = 25 cm2^2; New area: 152=22515^2 = 225 cm2^2.
  3. 3
    Area factor: 22525=9=32\dfrac{225}{25} = 9 = 3^2.

Answer

The area increases by a factor of 99.
When linear dimensions are scaled by factor kk, area scales by k2k^2. This is because area depends on two linear dimensions (both multiplied by kk). So scaling sides by 33 multiplies area by 32=93^2 = 9.

About Scaling

Changing the size of a quantity by multiplying by a factor, making it proportionally larger (factor >1> 1) or smaller (factor <1< 1).

Learn more about Scaling →

More Scaling Examples

Example 1 easy

A map has a scale of [formula]. Two cities are [formula] cm apart on the map. What is the actual dis

Example 2 medium

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Example 3 easy

A model car is built at a scale of [formula]. The model is [formula] cm long. How long is the actual

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