[David Sklansky]

Here is the way that requires neither geometrical ingenuity nor taking second derivatives of trigonemetric functions. (If Tom Cowley does that again his reign here will be short lived.)

Take a string six inches long and attach the ends. Thumbtack a potion of it on a horizontal line.Pull the rest up to make a triangle and notice that it is highest, and thus has greatest area, when it is isosceles.

Draw your altitude to form two right trianges. The hyptenuse (H) and the right triangle's base (b) add up to 3, half the perimeter. The area of the original triangle is the altitude times the right triangle's base.

The Pythagorean Theorem tells us that the altitude is the square root of [(3-b)squared - b squared]. Which is the square root of (9-6b).

So the area of the isosceles triangle is the square root of (9b squared -6b cubed).

The derivative of that is (18b-18b squared)/2 blah blah blah. Setting that derivative equal to zero we reduce to 18b = 18. b=1. Area is at a maximum when the triangle is 2 by 2 by 2.