Francis has 36 inches of string. What are the dimensions of the rectangle of greatest area that he can outline with the string? What is its area?

It so happens that for any definite perimeter, the largest rectangular area that

you can enclose with it is a square. That also means that for any definite area,

the rectangle with the shortest perimeter that can enclose it is a square.

You have to trust me on this ... in order to prove it or demonstrate it, we'd

need to get into Calculus, and nobody wants that!

But knowing it, we immediately know that the greatest rectangular area that

Francis can enclose with his 36 inches of string is a square, 9-inches on each

side. Its area is 81 square inches.

Dimensions: 9 by 9 by 9 by 9.

Area: 81