To find the ratio of the perimeter of the smaller square to the perimeter of the larger square, we first calculate the perimeter of each square.
The formula for the perimeter \( P \) of a square is given by: \[ P = 4 \times \text{side length} \]
For the smaller square with a side length of 2 centimeters: \[ P_{\text{small}} = 4 \times 2 = 8 \text{ cm} \]
For the larger square with a side length of 6 centimeters: \[ P_{\text{large}} = 4 \times 6 = 24 \text{ cm} \]
Now, we can find the ratio of the perimeter of the smaller square to the perimeter of the larger square: \[ \text{Ratio} = \frac{P_{\text{small}}}{P_{\text{large}}} = \frac{8}{24} \]
We simplify this fraction: \[ \frac{8}{24} = \frac{1}{3} \]
Thus, the ratio of the perimeter of the smaller square to the larger square is: \[ \boxed{\frac{1}{3}} \]
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