Question

1. What is the ratio of the perimeters of the larger figure to the smaller figure?

2. What is the ratio of the areas of the larger figure to the smaller figure?

HELP

Answer 1

Part 1) The ratio of the perimeters of the larger figure to the smaller figure is equal to
`(16)/(13)`

Part 2) The ratio of the areas of the larger figure to the smaller figure is
`(256)/(169)`

Explanation:

Part 1) What is the ratio of the perimeters of the larger figure to the smaller figure?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Let

z-----> the scale factor

In this problem

The scale factor is equal to

`z=(32)/(26)`

Simplify

`z=(16)/(13)`

Remember

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The ratio of the perimeters of the larger figure to the smaller figure is equal to
`(16)/(13)`

Part 2) What is the ratio of the areas of the larger figure to the smaller figure?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

we have

`z=(16)/(13)`

so

`z^(2)=((16)/(13))^(2)=(256)/(169)`

therefore

The ratio of the areas of the larger figure to the smaller figure is
`(256)/(169)`