Mr peterson will buy 80 feet of fencing. The pieces of fence come in whole numbers of feet. His enclosure will be a rectangle and have 4 sides. If he wants to enclose the least area, what should be the length, width, and area?
The perimeter is: P = 2x + 2y = 80 The area is: A = x * y The area as a function of a variable is: A (x) = x * (40-x) Rewriting we have: A (x) = 40x-x ^ 2 We derive the function: A '(x) = 40-2x We equal zero and clear x: 40-2x = 0 2x = 40 x = 40/2 x = 20 feet The other dimension is: y = 40 - x y = 40 - 20 y = 20 feet The area will be: A = x * y A = 20 * 20 A = 400 feet ^ 2 Answer: The dimensions are: x = 20 feet y = 20 feet The area is: A = 400 feet ^ 2
