Question
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?
Enter the response as a fraction
Enter the response as a fraction
Answers
GPT-4o mini
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:
\[
\boxed{\frac{1}{8}}
\]
\[
P = 4 \times \text{side length}
\]
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:
\[
\boxed{\frac{1}{8}}
\]