A rug weaver wants to create a large rectangular rug. He has 34 linear feet of a material that he plans to use on the entire outside border of the rug. He wants to use all this material. So, the rug must have a perimeter of 34 feet. The weaver already has a design for a rectangular rug that is 9 feet long and 8 feet wide. This design would produce a rug with the correct perimeter. However, he wants to be sure the rug will cover as much of the floor as possible, so he starts to experiment with changing the length and width of the rug design. To maintain the 34-foot border of the rug, he follows this rule: Whenever he decreases one dimension by x feet, he increases the other dimension by the same amount, x feet, as shown below. The area of the rug the weaver will make can be expressed as a function of x, the amount of material removed from the 9-foot side and added to the 8-foot side. Write an equation for this function and explain your work