Among all the rectangles whose perimeters are 100 feet, find the dimensions of the one with maximum area

dimensions-area

#1

among all the rectangles whose perimeters are 100 feet, find the dimensions of the one with maximum area.

Answer:

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
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