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In the diagram, the smaller square has a side length of 2 centimeters and the larger square has a side length of 6 centimeters. What is the ratio of the perimeter of the smaller square to the larger square? Type your response as a reduced fraction.

(1 point)
the ratio of the perimeter of the smaller square to the larger square =

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Answer 1

To find the ratio of the perimeter of the smaller square to the larger square, we first need to calculate the perimeter of each square.

1. **Perimeter of the smaller square**:
- Side length = 2 cm
- Perimeter = 4 × side length = 4 × 2 = 8 cm

2. **Perimeter of the larger square**:
- Side length = 6 cm
- Perimeter = 4 × side length = 4 × 6 = 24 cm

3. **Ratio of the perimeters**:
- Ratio = Perimeter of smaller square : Perimeter of larger square = 8 : 24

4. **Reducing the ratio**:
- We can simplify 8 : 24 by dividing both numbers by their greatest common divisor, which is 8.
- 8 ÷ 8 = 1
- 24 ÷ 8 = 3

Therefore, the ratio of the perimeter of the smaller square to the larger square is \( \frac{1}{3} \).