Final answer:
The length of fence needed to create a border for the fountain with a base area of 144 ft² is 48 ft.
Step-by-step explanation:
The area of the square fountain's base is given as 144 ft². Since the base of the fountain is a square, the area of the square is equal to the side length squared. So, if we let 'x' represent the length of one side of the square, we have the equation x² = 144. To find the length of one side, we take the square root of both sides of the equation, giving us x = √144. The square root of 144 is 12, so the length of one side of the square base is 12 ft.
To create a border around the fountain, we need to find the perimeter of the square base. The perimeter of a square is equal to four times the length of one side. In this case, the perimeter is 4 * 12 ft = 48 ft. Therefore, the length of fence needed to create a border for the fountain is 48 ft.