Question

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

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