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.

Question

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

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: \[ \text{Perimeter} = 4 \times \text{side length} = 4 \times 2 \text{ cm} = 8 \text{ cm} \]

2. Perimeter of the larger square: \[ \text{Perimeter} = 4 \times \text{side length} = 4 \times 6 \text{ cm} = 24 \text{ cm} \]

Now we can find the ratio of the perimeter of the smaller square to the perimeter of the larger square: \[ \text{Ratio} = \frac{\text{Perimeter of smaller square}}{\text{Perimeter of larger square}} = \frac{8 \text{ cm}}{24 \text{ cm}} = \frac{8}{24} \]

To simplify the fraction: \[ \frac{8}{24} = \frac{1}{3} \]

Thus, the ratio of the perimeter of the smaller square to the larger square is: \[ \boxed{\frac{1}{3}} \]