Thread: Getting min. value of this problem.

I'm confused with this problem:

What should be the shape of a rectangular field of a given area if it is enclosed by the least amount of fencing? Explain.

I know it's supposed to be rectangle, but I don't know how to create and equation that will explain it.

Someone pls. help.

Rule #1 - Name Stuff

It's a rectangle.

L = Length > 0
W = Width > 0

Rule #2 - Dump Information from Your Brain

Perimeter(L,W) = 2*L + 2*W > 0

Area(L,W) = L*W > 0

If anything else ABOUT RECTANGLES comes to mind, write it down, too.

Rule #3 Search for clues.

"field of a given area" -- Aha! Here is a parameter that doesn't move around. This gives:

L = Area/W (Or W = Area/L if you like. I'll use the first.)

and

Perimeter(W) = 2*(Area/W) + 2*W

I suspect you can now minimize Perimeter(W) with respect to the single variable "W".

Finally, you must ask how W relates to L. This is the exciting part of the problem!