Question

farmer joe is enclosing a rectangular area on his arm for his chicken with 200 feet of fencing that he recently acquired in a trade. two equal lengths of fencing, of unknown length x ft, will run perpendicular to the side of the barn, and a single length of fencing of unknown length (200-2x) ft will run parallel to the side of the barn. to the nearest square foot, what is the maximum possible area that joe can enclose with his 200ft of fencing

Answer 1

For this case, the area is given by:
 A = x * (200-2x)
 Rewriting:
 A = 200x-2x ^ 2
 Deriving the expression we have:
 A '= 200-4x
 Equaling zero we have:
 200-4x = 0
 We clear x:
 4x = 200
 x = 200/4
 x = 50 feet
 Then, the maximum area is:
 A (50) = 50 * (200-2 * 50)
 A (50) = 5000 feet ^ 2
 Answer:
 the maximum possible area that can be enclosed with his 200ft of fencing is:
 A (50) = 5000 feet ^ 2