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.

Question

(1 point)

Answer 1

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:

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

1. Perimeter of the smaller square:

   • Side length = 3 cm
   • Perimeter = \( 4 \times 3 = 12 \) cm

2. Perimeter of the larger square:

   • Side length = 24 cm
   • Perimeter = \( 4 \times 24 = 96 \) cm

Next, we need to compare the perimeters of the two squares and calculate the ratio of the perimeter of the smaller square to the perimeter of the larger square.

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

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

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

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

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