Question

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?

Answer 1

Let 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 = 160-3/2x

so, area = xy = 160x - 3/2(x^2)

now, using differentiation, find points where d(area)/dx has maxima.

Answer 2

How is differentiation to be used?

Answer 3

Do you mean like ax^2+bc+c=0

Answer 4

Please help

Answer 5

Yeah, 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

Answer 6

Suppose 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 = 160-3/2x

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?