Final Answer:
If the ratio of the side lengths of two similar polygons is 3:1, what is the ratio of the perimeters:
D. 9:1
Step-by-step explanation:
When two polygons are similar, their corresponding side lengths form a ratio that remains constant. If the ratio of the side lengths of two similar polygons is 3:1, then the ratio of their perimeters will be equal to the ratio of their side lengths.
The perimeter of a polygon is the sum of all its side lengths. If the ratio of the side lengths is 3:1, the ratio of the perimeters will also be 3:1 because for each unit increase in the side length ratio, there will be a proportional increase in the corresponding unit of the perimeter ratio.
Here's why the answer is 9:1:
Let's consider two similar polygons with side length ratios of 3:1. If the larger polygon has a side length of 3x and the smaller one has a side length of x, their perimeters will be 3x * number of sides for the larger polygon and x * number of sides for the smaller polygon. Thus, the ratio of their perimeters will be 3x * number of sides : x * number of sides = 3:1. Simplifying this further, 3x:x = 3:1. Consequently, the correct ratio of the perimeters of these polygons is 9:1.
Therefore, the ratio of the perimeters of two similar polygons with side length ratios of 3:1 is 9:1.