Problema Solution
The back of Jake's property is a creek. Jake would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 160 feet of fencing available, what is the maximum possible area of the corral?
Answer provided by our tutors
Let 'x' and 'y' represent the dimensions of the rectangular corral and lets assume that creek goes by the y side (we will not be needing fencing there).
The perimeter of the fencing is:
2x + y = 160
y = 160 - 2x
The area of the corral is:
A = x*y
plug y = 160 - 2x into the last equations:
A = x(160 - 2x)
A = 160x - 2x^2
We need to find the maximum for the parabolic function A = 160x - 2x^2:
The function has maximum since the quotient in front of x^2 is negative: -2 < 0
A max = c - b^2/4a, where a = -2, b = 160, c = 0
A max = 0 - 160^2/(4*(-2))
A max = 3,200 ft^2
The maximum possible area of the corral is 3,200 feet square.