In the diagram, the smaller square has a side length of 3 centimeters, and the larger square has a side length of 24 centimeters. Calculate and compare the perimeters of the similar squares. What is the ratio of the small square to the larger square?

Question

Enter the response as a fraction

Answer 1

To find the perimeters of the squares, we use the formula for the perimeter of a square, which is given by:

\[ P = 4 \times \text{side length} \]

For the smaller square:

• Side length = 3 cm
• Perimeter of the smaller square:

\[ P_{\text{small}} = 4 \times 3 = 12 \text{ cm} \]

For the larger square:

• Side length = 24 cm
• Perimeter of the larger square:

\[ P_{\text{large}} = 4 \times 24 = 96 \text{ cm} \]

Now, we need to find the ratio of the perimeters of the smaller square to the larger square:

\[ \text{Ratio} = \frac{P_{\text{small}}}{P_{\text{large}}} = \frac{12}{96} \]

To simplify this fraction, we divide both the numerator and the denominator by 12:

\[ \frac{12}{96} = \frac{1}{8} \]

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

\[ \boxed{\frac{1}{8}} \]