# How do I find an optimal rectangular area?

Jun 18, 2018

A square has the optimal rectangular area.

#### Explanation:

Find the area function, then maximize value.

Find the area function in one variable, so if you have $200$ feet perimeter, your sides of the rectangle are $x$ and $100 - x$. (remember two sides is half of the $200$).

$A = 100 x - {x}^{2}$

The maximum $x$ value occurs at

$x = - b \text{/} 2 a \implies x = 50$

So then the other side will be $50$ as well, so you have four sides totaling $200$.

Answer attributed to dear David Britz, who for some reason didn't post an answer and left a comment for us to see this question again and again.