How do I find an optimal rectangular area?

1 Answer
Jun 18, 2018

Answer:

A square has the optimal rectangular area.

Explanation:

Find the area function, then maximize value.

Find the area function in one variable, so if you have #200# feet perimeter, your sides of the rectangle are #x# and #100-x#. (remember two sides is half of the #200#).

#A=100x-x^2#

The maximum #x# value occurs at

#x=-b"/"2a => x = 50#

So then the other side will be #50# as well, so you have four sides totaling #200#.

Answer attributed to dear David Britz, who for some reason didn't post an answer and left a comment for us to see this question again and again.