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.

$\text{Ratio of perimeters}=\dfrac{10\ in.}{14\ in.}$

$\text{Ratio of perimeters}=\dfrac{5}{7}$

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

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

$\text{Ratio of areas}=\dfrac{(10)^2}{(14)^2}$

$\text{Ratio of areas}=\dfrac{100}{196}$

$\text{Ratio of areas}=\dfrac{25}{49}$

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

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