SOLUTION: Hi; I was hoping someone could help me with this problem. Maximum area. Jason plans to fence a rectangular area with 100 meters of fencing. He has written the formula A = w(50

Question 333504: Hi; I was hoping someone could help me with this problem.
Maximum area. Jason plans to fence a rectangular area with 100 meters of fencing. He has written the formula A = w(50 - w) to express the area in terms of the width w. What is the maximum possible area that he can enclose with his fencing?
Just by "guessing" I come up with a width of 25m and a length of 25 meters. How do I figure area? The answer in the back of the book says it's 625 meters, but I don't know how they got this.
Help please?!??

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jason plans to fence a rectangular area with 100 meters of fencing. He has written the formula A = w(50 - w) to express the area in terms of the width w. What is the maximum possible area that he can enclose with his fencing?
------------------------------------
A = w(50-w)
A = 50w-w^2
-w^2++50w
a = -1 ; b = 50
----
Maximum area occurs when w = -b/2a = -50/(2*-1) = 25
-----
Then 50-w = 25
---------
Maximum area = 25*25 = 625 sq meters
====================================
Cheers,
Stan H.
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