Randy is building a rectangular, fenced dog run beside his barn. he has 120m if fencing and plans to use the side of the barn as one side of fenced area. what are the dimensions of a dog run that maximizes the area randy can enclose

The answer is 1600m2 assuming the side of the barn is at least 40 meters long.
An enclosure is usually a parallelogram and since you already have one side you need to make three more. If you dive 120m by 3 you get 40m. Each wall will be 40m. The enclosure ends up being a square and a formula for a square is base times height, therefore the dimensions of the enclore would be 40m times 40m which gives you the answer of 1600m2.