Maximum Area of a Rectangle with Fixed Perimeter

Maximum Area of a Rectangle with Fixed Perimeter

For a rectangle with fixed perimeter $$p$$, the maximum area occurs when it is a square.

If its sides are $$x$$ and $$y$$:

$$2(x+y)=P$$

and maximum area is:

$$A_{\max}=\frac{P^2}{16}$$

Usage

- Used in standard geometric optimization problems.