Question

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

Answer 1

Answer:

Your answer would be  

a.

3:5; 3:5

Step-by-step explanation:

Answer 2

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