10 of 2210 of 22 Items

Question

Question

In the diagram, the smaller square has a side length of 2 centimeters and the larger square has a side length of 6 centimeters. What is the ratio of the perimeter of the smaller square to the larger square? Type your response as a reduced fraction.

(1 point)
the ratio of the perimeter of the smaller square to the larger square =

Skip to navigation

Answer 1

To find the ratio of the perimeter of the smaller square to the larger square, we first need to calculate the perimeter of each square.

1. Perimeter of the smaller square:

   • Side length = 2 cm
   • Perimeter = 4 × side length = 4 × 2 = 8 cm

2. Perimeter of the larger square:

   • Side length = 6 cm
   • Perimeter = 4 × side length = 4 × 6 = 24 cm

3. Ratio of the perimeters:

   • Ratio = Perimeter of smaller square : Perimeter of larger square = 8 : 24

4. Reducing the ratio:

   • We can simplify 8 : 24 by dividing both numbers by their greatest common divisor, which is 8.
   • 8 ÷ 8 = 1
   • 24 ÷ 8 = 3

Therefore, the ratio of the perimeter of the smaller square to the larger square is \( \frac{1}{3} \).