Question

The areas of two similar octagons are 112 in.² and 63 in.². What is the ratio (larger to smaller) of their perimeters?

16/3
4/9
16/9
4/3,

Answer 1

The answer is k = 4/3You have to consider the definition of "k"
k = growth factor (k> 1) or reduction (k <1)

Area1= (k ^ 2) * Area2Perimeter1 = k * Perimeter2
Substitute: 12 = (k ^ 2) * 63 k = sqaure root (112/63) k = 4/3

Answer 2

When the figures are similar, we have by definition:
For the area:
A1 = (k ^ 2) * A2
For the perimeter
P1 = k * P2
Note: The factor k is the same in both cases
Where,
k = growth factor (k> 1) or reduction (k <1)
Substituting values we have:
12 = (k ^ 2) * 63
Let's clear k:
k = root (112/63)
k = 4/3
Answer:
The ratio (larger to smaller) of their perimeters is:
k = 4/3