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?

Part 1) The ratio of the perimeters of the larger figure to the smaller figure is equal to

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

Step-by-step 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

Simplify

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

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

so

therefore

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

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!