1. **Problem Statement:** Suppose a square and an equilateral triangle have the same perimeter. Each side of the equilateral triangle is 6 centimeters longer than each side of the square. Find the length of each side of the square. 2. **Define variables:** Let the side length of the square be $s$ cm. Each side of the equilateral triangle is then $s + 6$ cm. 3. **Perimeter formulas:** - Perimeter of the square: $$P_{square} = 4s$$ - Perimeter of the equilateral triangle: $$P_{triangle} = 3(s + 6)$$ 4. **Set perimeters equal:** Since the perimeters are the same, $$4s = 3(s + 6)$$ 5. **Solve the equation:** $$4s = 3s + 18$$ Subtract $3s$ from both sides: $$4s - 3s = 18$$ $$s = 18$$ 6. **Interpretation:** The side length of the square is 18 cm. 7. **Check:** - Square perimeter: $4 \times 18 = 72$ cm - Triangle side length: $18 + 6 = 24$ cm - Triangle perimeter: $3 \times 24 = 72$ cm Both perimeters match, confirming the solution. **Final answer:** The length of each side of the square is $\boxed{18}$ cm.