Question

Theorem: For any given area A, the rectangle that has the least perimeter is a square.

Part I:

Complete the proof that is outlined below. Submit each step as part of your final answer.

Proof:

In terms of the side length, x, the formula for the perimeter of a square:
P=2x+((2A)/(x))

Define a new variable: v=sqrt(x)- ((sqrt(A))/(sqrt(x))

In terms of the new variable, v, compute and simplify: 2v^2 = _____.
Rewrite this equation to get the formula for P alone on one side. Replace the formula by the variable P. Write that result by completing the equation below:

P =