Final answer:
To find the dimensions of a rectangle with the largest area given a fixed perimeter of 160 ft, the shape is a square with each side measuring 40 ft.
Step-by-step explanation:
The student is asking how to find the dimensions of a rectangle with a maximum area given a fixed perimeter of 160 ft. To maximize the area of a rectangle with a given perimeter, the rectangle must be a square. To find the dimensions of this square, we use the fact that a square has four equal sides. If the perimeter is 160 ft, each side of the square would be 160 ft divided by 4.
Perimeter (P) of a square is 4 times the side length (s), so P = 4s. Given a perimeter of 160 ft, we set up the equation 160 = 4s. Dividing both sides by 4, we find that s = 40 ft. Consequently, each side of the rectangle that will yield the largest area, which is actually a square in this case, will be 40 feet.