Final answer:
The dimensions of the rectangle with a perimeter of 148 feet that has the maximum area would be 37 feet by 37 feet, forming a square. The maximum area of the rectangle is 1369 square feet.
Step-by-step explanation:
To find the dimensions of a rectangle with a known perimeter and the maximum area, first understand that the rectangle with the maximum area is a square. In this case, the perimeter is 148 feet.
To calculate the side length of the square, divide the perimeter by 4. Thus, the side of the square would be 148 feet / 4 = 37 feet. Therefore, the maximum area will be achieved when each side of the rectangle is 37 feet long, making it a square with these dimensions.
The maximum area of such a rectangle, which in this case is a square, is obtained by squaring the side length: Area = side × side = 37 feet × 37 feet = 1369 square feet.