How do you find the maximum area of a rectangle with perimeter of 40 ft?

1 Answer
MeneerNask
Feb 9, 2016

Your gut feeling may tell you it's a square, with sides 10 ft, or a total area of 100 sqft.

Explanation:

You can divert from this and see if the area gets any larger, or you can use the mathematical way:
If the length =#x# and the width =#y# then the perimeter #P=40#
#P=2x+2y=40->x+y=20->y=20-x#

As for the area #A#:
#A=x*y=x*(20-x)=20x-x^2#
And we have to find an extreme for that:
We can do this by setting the derivative to #=0#
#A'=20-2x=0->x=10->y=10#
Just as we thought in the first place.
graph{20x-x^2 [-131.6, 135.4, -8.4, 125.1]}

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