To find the ratio of the perimeter of the smaller square to the perimeter of the larger square, we first need to calculate the perimeters of both squares.
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: \[ P_{\text{small}} = 4 \times 2 = 8 \text{ centimeters} \]
For the larger square with a side length of 6 centimeters: \[ P_{\text{large}} = 4 \times 6 = 24 \text{ centimeters} \]
Now, we find the ratio of the perimeter of the smaller square to the perimeter of the larger square: \[ \text{Ratio} = \frac{P_{\text{small}}}{P_{\text{large}}} = \frac{8}{24} \]
To reduce this fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 8: \[ \frac{8}{24} = \frac{8 \div 8}{24 \div 8} = \frac{1}{3} \]
Thus, the ratio of the perimeter of the smaller square to the larger square is: \[ \boxed{\frac{1}{3}} \]
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