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.

Answer 1

To calculate the perimeters of the smaller and larger squares, we use the formula for the perimeter of a square, which is given by:

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

1. Calculate the perimeter of the smaller square:

   • Side length = 3 cm \[ \text{Perimeter of smaller square} = 4 \times 3 = 12 \text{ cm} \]

2. Calculate the perimeter of the larger square:

   • Side length = 24 cm \[ \text{Perimeter of larger square} = 4 \times 24 = 96 \text{ cm} \]

3. Find the ratio of the perimeter of the smaller square to the larger square: \[ \text{Ratio} = \frac{\text{Perimeter of smaller square}}{\text{Perimeter of larger square}} = \frac{12}{96} \]

4. Simplify the fraction: \[ \frac{12}{96} = \frac{1}{8} \]

Therefore, the ratio of the perimeters of the smaller square to the larger square is

\[ \boxed{\frac{1}{8}} \]