Final answer:
The greatest possible area of a rectangular pen enclosed by a given length of fencing can be achieved when the rectangular pen is a square.
Step-by-step explanation:
The greatest possible area of a rectangular pen enclosed by a given length of fencing can be achieved when the rectangular pen is a square. In a square, all sides are equal in length, so the given length of fencing would be divided equally among all four sides. To find the maximum area, divide the length of the fencing by 4 to get the length of one side of the square. Then, multiply this length by itself to find the area of the square.
For example, if you have 80 feet of fencing, divide it by 4 to get 20 feet as the length of one side of the square. Then, multiply 20 feet by itself to get 400 square feet as the maximum possible area