among all the rectangles whose perimeters are 100 feet, find the dimensions of the one with maximum area.
Let 100=2L+2W (perimeter) and A=LW (area). Then we want to maximize A. But it has 2 variables instead of 1. Luckily we can use our perimeter equation to express one variable in terms of the other: W=50−L. Plugging this into the area equation, we get the single variable function