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 ratio of the areas of two similar figures is the square of the ratio of their corresponding side lengths.
Let the ratio of the side lengths be x, then the ratio of the areas is x². Therefore, x² = 112/63 = 16/9.
Since the octagons are similar, the ratio of their perimeters would be the same as the ratio of their side lengths, which is √(16/9) = 4/3.
Therefore, the ratio of the larger octagon's perimeter to the smaller octagon's perimeter is 4/3.