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