Please help me solve this problem:

Question: One-hundred (100) feet of fence is used to fence in a rectangular yard. Find the length and width that give maximum area.

Thanks in advance for your assistance.

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- Feb 4th 2008, 02:37 PMcurrypuffMaximum Area of a Rectangle
Please help me solve this problem:

Question: One-hundred (100) feet of fence is used to fence in a rectangular yard. Find the length and width that give maximum area.

Thanks in advance for your assistance. - Feb 4th 2008, 04:23 PMwinglessCode:
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x

Formula for the area is, .

As ,

So our formula becomes, .

To find the extremum point, we will differentiate it and will give us the extremum point.

There's an extremum point at , but we don't know whether it's a minima or a maxima. The second derivative test will help us to determine what it is :)

If , then it's a minima. If , it's a maxima.

, which is less than 0 and which makes our point a maxima :)

So will give us the maximum area. - Feb 4th 2008, 07:00 PMinvite_moon
x+y=50

so

50=x+y>=2*sqrt(x*y) (when x=y then x+y=sqrt(x*y))

so we have x*y<=25^2=625 (when x=y=25)

Calculus is unnecessary - Feb 5th 2008, 12:06 AMwingless