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?

Answer 1

To calculate the perimeters of both squares, we use the formula for the perimeter of a square, which is given by:

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

First, we calculate the perimeter of the smaller square with a side length of 13 centimeters:

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

Next, we calculate the perimeter of the larger square with a side length of 39 centimeters:

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

Now, we compare the perimeters of the two squares and calculate the ratio of the perimeter of the larger square to that of the smaller square:

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

To simplify this ratio, we divide both the numerator and the denominator by 52:

\[ \frac{156}{52} = 3 \]

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

\[ \boxed{3} \]