Question

If the scale factor between a scale drawing of a rectangle and the real object is 1:3 what would be the ratio of the areas?

Answer 1

The ratio of the areas will be will be 1 : 9

Explanation:

The linear scale factor represents a ratio that is used to multiply the dimensions of objects so that accurate geometries can be transferred between real-life and paper.

The linear scale factor is quite different from the area scale factor but related to it in the following way:

The area factor can be obtained by squaring the linear scale factor.

This is Area factor = (Linear scale factor) ^2.

Linear scale factor = (1:3)

Area factor =
`1^2 : 3^2`

Area factor will be 1: 9

Thus, when the linear scale factor is 1:3 the area factor will be 1 : 9