Use the image to answer the question.

Question

One smaller and one larger square side by side.

In the diagram, the smaller square has side lengths of 13 centimeters, and the larger square has side lengths of 39 centimeters. Calculate and compare the perimeters. What is the ratio of the perimeter of the larger square to the smaller square?

(1 point)
Responses

31
Start Fraction 3 over 1 End Fraction

34
Start Fraction 3 over 4 End Fraction

43
Start Fraction 4 over 3 End Fraction

13

Answer 1

To calculate the perimeters of the squares, we use the formula for the perimeter of a square, which is \( P = 4 \times \text{side length} \).

1. Perimeter of the smaller square:

   • Side length = 13 cm
   • \( P_{small} = 4 \times 13 = 52 \) cm

2. Perimeter of the larger square:

   • Side length = 39 cm
   • \( P_{large} = 4 \times 39 = 156 \) cm

3. Ratio of the perimeter of the larger square to the smaller square: \[ \text{Ratio} = \frac{P_{large}}{P_{small}} = \frac{156}{52} = 3 \]

So, the ratio of the perimeter of the larger square to the smaller square is \( \frac{3}{1} \) or \( 3 \).

The correct response is: Start Fraction 3 over 1 End Fraction.