Question

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 =

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:
\[
\boxed{\frac{1}{3}}
\]