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If the ratio of the sides of two squares is 3:1, what is the ratio of their perimeters?

- 3:1
- 4:1
- 9:1
- 12:1

1 Answer

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Final answer:

The ratio of the perimeters of two squares with a side length ratio of 3:1 is also 3:1, as the perimeter is directly proportional to the side length.Option A is the correct answer.

Step-by-step explanation:

If the ratio of the sides of two squares is 3:1, the ratio of their perimeters is also 3:1. Since the perimeter of a square is the sum of all its sides (4 times the length of one side), if the lengths of the sides are in a 3:1 ratio, the perimeters will maintain that same ratio.

To understand this, consider a square with a side length of 'a'; its perimeter will be 4a.

If another square has sides that are three times longer, that is '3a', its perimeter will be 4 times '3a', or 12a. Hence, the ratio between the perimeters of the two squares remains at 3:1 because 12a to 4a simplifies to 3:1.

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