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in the diagram the smaller square has a side length of 3 centimeters and the larger square has a side length of 24 centimeters calculate and compare the perimeters of the similar squares what is the ratio of the small square to the larger square enter your response as a fraction
Responses

3/24
3/24

1/8
1/8

1/3
1/3

9/81
9/81
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1 answer

To calculate the perimeters of the squares, we can use the formula for the perimeter of a square, which is:

\[ P = 4 \times \text{side length} \]

For the smaller square:

  • Side length = 3 cm
  • Perimeter = \( 4 \times 3 = 12 \) cm

For the larger square:

  • Side length = 24 cm
  • Perimeter = \( 4 \times 24 = 96 \) cm

Now, we can find the ratio of the perimeters of the smaller square to the larger square:

\[ \text{Ratio} = \frac{\text{Perimeter of smaller square}}{\text{Perimeter of larger square}} = \frac{12}{96} = \frac{1}{8} \]

So, the final answer is:

1/8