Find the similarity ratio and the ratio of the perimeters of two regular octagons with areas of 18 in2 and 50 in2.

By definition we have that the area of a regular octagon is:

A = 4.83L ^ 2

Where, L is the length of the octagon side.

the similarity ratio = the area ratio.

We have then:

similarity ratio = (50) / (18) = 25/9.

the ratio of the perimeters

A1 = 4.83L1 ^ 2

L1 ^ 2 = A1 / 4.83

L2 ^ 2 = A2 / 4.83

L1 ^ 2 / L2 ^ 2 = A1 / A2 = 25/9

L1 / L2 = 5/3

The perimeter is:

P1 = 8L1

P2 = 8L2

P1 / P2 = 8L1 / 8L2 = L1 / L2 = 5/3

answer:

similarity ratio:

25: 9

the ratio of the perimeters:

5: 3