In a 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 ratios of the perimeter of the larger square to the smaller square? put the answer as a fraction

Answer 1

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

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

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

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

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

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

Now, to find the ratio of the perimeter of the larger square to the perimeter of the smaller square, we set up the ratio:

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

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

\[ \frac{156 \div 52}{52 \div 52} = \frac{3}{1} = 3 \]

Thus, the ratio of the perimeter of the larger square to that of the smaller square is:

\[ \frac{3}{1} \]

So, the final answer is \(\frac{3}{1}\).