Question

The pair of figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas .

Answer 1

Given:

The pair of similar triangles.

Base of smaller triangle = 10 in

Base of larger triangle = 14 in

To find:

The ratio of the perimeters and the ratio of the areas.

Solution:

Ratio of perimeter of similar triangles is equal to the ratio of their corresponding sides.

`\text{Ratio of perimeters}=(10\ in.)/(14\ in.)`

`\text{Ratio of perimeters}=(5)/(7)`

`\text{Ratio of perimeters}=5:7`

The ratio of area of similar triangles is equal to the ratio of squares of their corresponding sides.

`\text{Ratio of areas}=((10)^2)/((14)^2)`

`\text{Ratio of areas}=(100)/(196)`

`\text{Ratio of areas}=(25)/(49)`

`\text{Ratio of areas}=25:49`

Therefore, the ratio of the perimeters is 5:7 and the ratio of the areas 25:49.