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?

Question

(1 point)
Responses

43
Start Fraction 4 over 3 End Fraction

34
Start Fraction 3 over 4 End Fraction

31
Start Fraction 3 over 1 End Fraction

13

Answer 1

To find the perimeters of the squares, we can use the formula for the perimeter of a square, which is:

$$\text{Perimeter}=4\times \text{side length}$$

For the smaller square with a side length of 13 centimeters:

$$\text{Perimeter of smaller square}=4\times 13=52\text{ centimeters}$$

For the larger square with a side length of 39 centimeters:

$$\text{Perimeter of larger square}=4\times 39=156\text{ centimeters}$$

Next, we calculate the ratio of the perimeter of the larger square to the perimeter of the smaller square:

$$\text{Ratio}=\frac{\text{Perimeter of larger square}}{\text{Perimeter of smaller square}}=\frac{156}{52}$$

Calculating the ratio:

$$\frac{156}{52}=3$$

Thus, the ratio of the perimeter of the larger square to the smaller square is $\frac{3}{1}$.

The correct response is:

31 (Start Fraction 3 over 1 End Fraction)