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,

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

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