Final answer:
To find the perimeter of the square, we can start by finding the dimensions of the equilateral triangle. It is given that each side of the triangle is 4 inches longer than each side of the square. By equating the perimeters of the triangle and the square, we can determine the side length of the square and calculate its perimeter.
Step-by-step explanation:
To find the perimeter of the square, we can start by finding the dimensions of the equilateral triangle. It is given that each side of the triangle is 4 inches longer than each side of the square. Let x be the side length of the square. Therefore, the side length of the equilateral triangle would be x+4. Since all sides of an equilateral triangle are equal, the perimeter of the triangle would be 3(x+4). But it is also given that the triangle and square have the same perimeter, so we can equate the two:
x + x + x + x = 3(x+4)
Simplifying the equation, we get:
4x = 3x + 12
Subtracting 3x from both sides, we get:
x = 12
So, the side length of the square is 12 inches. Since the perimeter of a square is given by 4 times the side length, the perimeter of the square would be 4 * 12 = 48 inches.