### Instruction: Wendy has 180 feet of fencing. She needs to enclose a rectangular space with an area that is ten times its perimeter. If she uses up all her fencing material, how many feet is the largest side of the enclosure?### Response: I need to find the dimensions of a rectangle that has a perimeter of 180 feet and an area of 10 times that, or 1800 square feet.
Let me call the length and width of the rectangle x and y, respectively.
Then I have two equations relating x and y: 2x + 2y = 180 and xy = 1800.
I can simplify the first equation by dividing both sides by 2, getting x + y = 90.
Then I can substitute y = 90 - x into the second equation, getting x(90 - x) = 1800.
This is a quadratic equation that I can solve by expanding, rearranging, and factoring.
I get x^2 - 90x + 1800 = 0, which factors into (x - 60)(x - 30) = 0.
So x is either 60 or 30, and y is either 30 or 60, depending on which one I choose for x.