PLEASE HELP!! 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:

Define a new variable:

In terms of the new variable, v, compute and simplify: 2v2 = .
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 = 2v2 +

Part II:

In the equation above, P is a function of v, and A is a constant. The minimum value of this function occurs when v = .
Explain why this is true.
Substitute this value of v into and solve for x.
This is the value of the length x that yields the minimum value of P. For this length, what is the value of the width?
How do the length and width compare?