Final answer:
The ratio of the perimeters of two similar rectangles with a side-length ratio of 1/3 is also 1/3. The sides of the smaller rectangle are one-third of the corresponding sides of the larger rectangle, thus the perimeter, which is the sum of all sides, will maintain the same ratio.
Step-by-step explanation:
If two similar rectangles have a side-length ratio of 1/3, then the ratio of their perimeters is also 1/3.
To understand why, let's consider that the rectangles are similar, which means their corresponding sides are proportional.
If one rectangle has sides of length L and W, then the similar rectangle would have sides of lengths L/3 and W/3, given the side-length ratio of 1/3.
The perimeter of the first rectangle is 2L + 2W, and the perimeter of the second, smaller rectangle is 2(L/3) + 2(W/3) = (2L/3) + (2W/3).
Simplifying this, we get 2/3(L + W), which means the perimeter of the smaller rectangle is 1/3 of the larger rectangle. This ratio remains constant because the rectangles are similar and their sides are scaled by the same factor.