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?

Answer 1

To calculate the perimeter of each square, 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
   • \( P_{\text{small}} = 4 \times 13 = 52 \) cm

2. Perimeter of the larger square:

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

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

\[ \text{Ratio} = \frac{P_{\text{large}}}{P_{\text{small}}} = \frac{156}{52} \]

Now we can simplify the ratio:

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

Thus, the ratio of the perimeter of the larger square to the smaller square is \( 3:1 \).

In summary:

• Perimeter of smaller square: 52 cm
• Perimeter of larger square: 156 cm
• Ratio of the perimeter of the larger square to the smaller square: 3:1.