Use the image to answer the question.

Question

One smaller and one larger square side by side.

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 your response as a fraction.

(1 point)

Answer 1

To calculate the perimeters of the squares, we can use the formula for the perimeter of a square:

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

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 find the ratio of the perimeters of the smaller square to the larger square:

\[ \text{Ratio of perimeters} = \frac{\text{Perimeter of smaller square}}{\text{Perimeter of larger square}} = \frac{12}{96} \]

To simplify this fraction:

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

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

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