Question

The figures below are similar.

12 yd
30 yd
What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the
smaller figure? The figures are not drawn to scale.

Answer 1

a) 2.5

b) 6.25

Explanation:

For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.

Application

The ratio of linear dimensions, larger to smaller, is ...

(30 yd)/(12 yd) = 2.5

a) Perimeter

Perimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.

b) Area

The ratio of areas, larger to smaller, is the square of the scale factor for side lengths:

(2.5)² = 6.25

The ratio of the areas of the larger to smaller figure is 6.25.