Hello, integral0!

**Quote:**

Suppose you have to use exactly 200 m of fencing to make either one square enclosure

or two separate square enclosures of any sizes you wish.

What plan gives you the least area? the greatest area?

Let the two squares have sides

*x* and

*y*.

The total area of the two squares is:

The two squares will have a total perimeter of

Hence,

Substituting into the area function:

So, we have:

Then

Since

the graph is concave upward.

Hence, with two 25-meter squares, we have

*minimum* area:

Any other value of

*x* will produce a larger area.

So at the very extreme, we can let

and have one square with a

*maximum* area of