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anonymous
 5 years ago
Suppose that 320 feet of fencing are available to enclose a rectangular field and that one side of the field must be given double fencing. What are the dimensions of the field of maximum area?
anonymous
 5 years ago
Suppose that 320 feet of fencing are available to enclose a rectangular field and that one side of the field must be given double fencing. What are the dimensions of the field of maximum area?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let one side be x, and the other side be y. Now, let the side with double fencing be x. So, the perimeter is 3x + 2y, which is given to be 320. We need to maximize the area, which is xy. From the perimeter, y = 1603/2x so, area = xy = 160x  3/2(x^2) now, using differentiation, find points where d(area)/dx has maxima.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How is differentiation to be used?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you mean like ax^2+bc+c=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, just like that. Find out values of x where d(area)/dx is zero. You can differentiate the area expression the same way you would differentiate a generic quadratic expression like ax^2+bx+c. The area expression I mentioned above can be written like ax^2 + bx + c, where a = 3/2 b = 160 c = 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Suppose that a rectangular area is to be fenced, except one side must be fenced twice because it runs along a river. If the amount of fencing is 320 yards in length, what is the maximum area that can be fenced? I see this question answered below, but We need to maximize the area, which is xy. From the perimeter, y = 1603/2x so, area = xy = 160x  3/2(x^2)  why is this x squared? and once you derive the ax^2+bx+c=0 formula, how do you maximize the area?
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