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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.

The formula for the perimeter \( P \) of a square with side length \( s \) is:

\[
P = 4s
\]

1. For the smaller square with a side length of 2 centimeters:
\[
P_{\text{small}} = 4 \times 2 = 8 \text{ centimeters}
\]

2. For the larger square with a side length of 6 centimeters:
\[
P_{\text{large}} = 4 \times 6 = 24 \text{ centimeters}
\]

Now, we can find the ratio of the perimeter of the smaller square to the perimeter of the larger square:

\[
\text{Ratio} = \frac{P_{\text{small}}}{P_{\text{large}}} = \frac{8}{24}
\]

Now, we can simplify the fraction:

\[
\frac{8}{24} = \frac{1}{3}
\]

Thus, the ratio of the perimeter of the smaller square to the larger square is:

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