To calculate the perimeters of the smaller and larger squares, we can use the formula for the perimeter of a square, which is given by:
\[ \text{Perimeter} = 4 \times \text{side length} \]
For the smaller square:
- Side length = 3 cm
- Perimeter = \( 4 \times 3 = 12 \) cm
For the larger square:
- Side length = 24 cm
- Perimeter = \( 4 \times 24 = 96 \) cm
Now, we can compare the perimeters of the two squares and find the ratio of the smaller square's perimeter to the larger square's perimeter.
Ratio of the perimeters: \[ \text{Ratio} = \frac{\text{Perimeter of smaller square}}{\text{Perimeter of larger square}} = \frac{12}{96} \]
To simplify the fraction \( \frac{12}{96} \), we can divide both the numerator and denominator by 12:
\[ \frac{12 \div 12}{96 \div 12} = \frac{1}{8} \]
Thus, the ratio of the perimeter of the smaller square to the larger square is:
\[ \frac{1}{8} \]
In conclusion, the perimeters of the squares are \( 12 \) cm for the smaller square and \( 96 \) cm for the larger square, and the ratio of the smaller square's perimeter to the larger square's perimeter is \( \frac{1}{8} \).
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