The scale factor of two regular octagons is 5 : 2. Find the ratio of their perimeters and the ratio of their areas.

Answer 1

Let the side length of the smaller octagon be 2x, then the side length of the larger octagon is 5x.

The perimeter of the smaller octagon is 8(2x) = 16x.
The perimeter of the larger octagon is 8(5x) = 40x.
Therefore, the ratio of their perimeters is:

(Perimeter of larger octagon) : (Perimeter of smaller octagon) = 40x : 16x = 5 : 2.

The area of the smaller octagon is (1 + sqrt(2)) * (2x)^2 ≈ 9.66x^2.
The area of the larger octagon is (1 + sqrt(2)) * (5x)^2 ≈ 60.66x^2.
Therefore, the ratio of their areas is:

(Area of larger octagon) : (Area of smaller octagon) = 60.66x^2 : 9.66x^2 = 6.27 : 1.

Answer 2

the ratio of their perimeter, which is a linear measurement = 5 : 2

the ratio of their areas = 5^2 : 2^2 = 25 : 4

Answer 3

Sorry about that, you are correct. The ratio of their areas should be (5x)^2 : (2x)^2 = 25 : 4. Thank you for pointing that out!