How do you find the maximum area of rectangle with 80ft perimeter?
1 Answer
Algebraically, we can show that the maximum area of the rectangle is achieved when it is a square. In this case, the maximum area is
Explanation:
Since this is not in calculus, I'll provide a non-calculus answer.
We know the rectangle always has a perimeter of
We also know that the area of the rectangle is
Use the perimeter expression
#A=lw#
#A=(40-w)w#
#A=-w^2+40w#
This quadratic function can be graphed, and the highest point will be the spot where the rectangle's area is maximized.
graph{-x^2+40x [-5, 45, -145, 460]}
The highest point, the vertex of the parabola, is
