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

43
Start Fraction 4 over 3 End Fraction

34
Start Fraction 3 over 4 End Fraction

13

1 answer

To calculate the perimeters of both 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 = 13 cm
  • Perimeter = \( 4 \times 13 = 52 \) cm

For the larger square:

  • Side length = 39 cm
  • Perimeter = \( 4 \times 39 = 156 \) cm

Now, to find the ratio of the perimeter of the larger square to the perimeter of the smaller square, we use: \[ \text{Ratio} = \frac{\text{Perimeter of larger square}}{\text{Perimeter of smaller square}} = \frac{156}{52} \]

Now, simplify \( \frac{156}{52} \):

  • \( 156 \div 52 = 3 \)

Thus, the ratio is \( 3 \) or \( \frac{3}{1} \).

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