Scale factor

A scale factor is a number by which a quantity is multiplied, changing the magnitude of the quantity. Scale factors are often used in geometric contexts, as part of figure models, and more.

The larger penguin model above is 3 times larger than the smaller penguin; To change the larger penguin into the smaller one, we would use a scale factor of . The pentagon shown in green is enlarged by a scale factor of 2 to produce the pentagon shown in blue.

Scaling geometric figures

The scale factor tells us what to multiply each side length of a geometric figure by to produce a scaled, similar figure.

Triangle ABC is similar to triangle DEF (△ABC~△DEF), which means that the corresponding side lengths of the triangles are proportional:

Any of the three ratios can be used to determine the scale factor.


Find the lengths of sides b and d for the triangles below given that △ABC~△DEF.

Since the triangles are similar, . We can find the scale factor using the ratio of a pair of corresponding sides: . This is the scale factor we multiply a side length of triangle ABC by to find its corresponding side length in DEF. We would multiply a side length of DEF by instead to find its corresponding side length in ABC.

We could also set the ratios of the corresponding sides equal to find b and d.

18d = 216
d = 12
24b = 360
b = 15