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+ Define a new variable: y = VA 1. In terms of the new variable, v, compute and simplify: 2 =, 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= 22 + Part Il: 1. In the equation above, P is a function of v, and A is a constant. The minimum value of this function occurs when v = 2. Explain why this is true. 3. Substitute this value of v into y = x - VA and solve for x. 4. 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? 5. How do the length and width compare?

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