SOLUTION: I'm having a difficult time with the following problem and would greatly appreciate help. The problem reads: I plan to fence my rectangular garden with 100 meters of fencing. I

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Question 689122: I'm having a difficult time with the following problem and would greatly appreciate help. The problem reads: I plan to fence my rectangular garden with 100 meters of fencing. I am using the function A=w(50-w) to express the area in terms of its width. What is the maximum possible area that I can enclose with this fencing?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The maximum area of a rectangle always ends
up being a square when you alter the lengths
of the sides. I will show this for your problem.

rewrite it

This is a parabola which has a maximum and
not a minimum. This is indicated by the minus sign
in front of the term
-------------------------
There are 2 equally valid ways to find the w-coordinate
of the peak ( maximum area ).
The peak will be midway between the roots which occur
when

This equation is true for 2 values of ,
, and
The peak will be midway between, at
------------------------------------------
The other way to find the maximum is to use the general
formula where the equation
has the form . Of course you have

( c = 0 )
You have

, so

--------------------
Now when you plug back into your equation,

which is the maximum area
Ntice that you have a square because
( formula for circumference )

m of fencing
hope this helps