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If two similar rectangles have a side-length ratio of 1/3, then the ratio of their perimeter is ____.

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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.

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