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Optimization, in pure mathematics, is the mathematical analysis of a problem with the goal of finding the most efficient solution. This usually involves maximizing or minimizing a cost function.
- , where P is a constant
This gives a quadratic equation. The precise value of the optimal length l can be found by taking the derivative of the equation and finding the root.
We can infer from this that the optimal rectangle is a square, as 2l = P/2, which requires w to also be P/4, making the length and width equal.