Final answer:
The length of each side of the square, when an equilateral triangle and square have the same perimeter and the triangle's side is 12 cm, is 9 cm.
Step-by-step explanation:
If an equilateral triangle and a square have the same perimeter, and one side of the triangle measures 12 cm, we can calculate the length of each side of the square by first determining the perimeter of the triangle. Since all sides of an equilateral triangle are equal, the triangle's perimeter is 12 cm × 3, which equals 36 cm. Knowing that the square and the triangle have the same perimeter, we can find the length of the square's side by dividing the perimeter by 4 (since a square has four equal sides).
The calculation is as follows:
Perimeter of square = Perimeter of equilateral triangle = 36 cm.
Length of each side of the square = Perimeter of square ÷ 4 = 36 cm ÷ 4 = 9 cm.
Therefore, each side of the square measures 9 cm.