Final answer:
To find the perimeter of the square, divide the perimeter of the equilateral triangle by 3 to find the side length of the triangle. Then multiply the side length of the triangle by 2 to find the side length of the square. Finally, multiply the side length of the square by 4 to find the perimeter of the square.
The perimeter of the square is found to be Option b: 44cm.
Step-by-step explanation:
- To find the perimeter of a square whose side is half of the side of the equilateral triangle, we first need to find the side length of the equilateral triangle.
- Since an equilateral triangle has all three sides equal, the perimeter of the triangle is 3 times the length of one side.
- Given that the perimeter of the triangle is 66 cm, we can divide it by 3 to find the length of one side, which is 22 cm.
- Since the side length of the square is half of the side length of the triangle, the side length of the square is 22 cm / 2 = 11 cm.
- The perimeter of a square is 4 times the length of one side.
- Therefore, the perimeter of the square is 4 * 11 cm = 44 cm.