Thread: Maximum 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.

Code:

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y|               |y
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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.

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

Originally Posted by invite_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)

Your solution is OK, but can you apply it to more complicated functions?

Originally Posted by invite_moon

Calculus is unnecessary

This question is posted under the Calculus forum, so I treated it like any optimization question.