The ratio of the areas of two similar figures is the square of the ratio of their corresponding side lengths. Thus, we can find the ratio of the lengths of corresponding sides of the two octagons by taking the square root of the ratio of their areas:
sqrt(112/63) = 1.5
This means that the corresponding sides of the larger octagon are 1.5 times longer than those of the smaller octagon. Therefore, the ratio of their perimeters is also 1.5:
Perimeter of larger octagon / Perimeter of smaller octagon = 1.5
Answer: The ratio of the larger octagon's perimeter to the smaller octagon's perimeter is 1.5.
The areas of two similar octagons are 112 in.² and 63 in.². What is the ratio (larger to smaller) of their perimeters?
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