1. ## largest area geometry

I got this assignment tomorrow and am having trouble.
"If you have 100 meters of fence, what are the dimensions of the maximum area you can enclose?"

"Also, if you want to enclose 100 square meters of land what is the maximum length of fence you can use?"

2. Originally Posted by AndrewT
...

"If you have 100 meters of fence, what are the dimensions of the maximum area you can enclose?"
The area with a minimum circumference is a circle. Thus the maximum area with a circumference of 100 m is a circle with a diameter of 31.83 m and the value of the area is 795.775 m²

"Also, if you want to enclose 100 square meters of land what is the maximum length of fence you can use?"
There doesn't exist a maximum length of the fence. If the area is a rectangle then you can calculate the length with respect to the width of the rectangle:

$l=\frac{100}{w}$

If w is becoming smaller and smaller l is growing more and more. In the end you need a fence of infinite length to enclose nothing.

3. Thanks man you are a life saver.

P.S you are really smart I could probably never figure thathttp://www.mathhelpforum.com/math-he...9-headbang.gif

4. Originally Posted by earboth
The area with a minimum circumference is a circle.

[snip]
A more interesting question is proving this. I'm happy to give a proof if there's an expression of interest.

5. Originally Posted by mr fantastic
A more interesting question is proving this. I'm happy to give a proof if there's an expression of interest.
5.5% VAT.

Or $\rm{interest}=\frac{\text{attention}}{\textrm{time }}$