SOLUTION: Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find th

Click here to see ALL problems on Inequalities

Question 139678: Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.

thank you
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
------------------
Draw the picture.
You have three lengths of fence; two are equal so call them "x": one
is not equal but it can be called 120-2x because it is the rest of
the fence after you have used up the two x's.
-------------------
EQUATION:
Area of the rectangle = x*(120-2x) = 120x-2x^2
----------
That is a quadratic with a=-2 and b = 120
------------
The maximum occurs when x = -b/2a = -120/(2*-2) = 30
--------------
So the two equal sides are each 30 ft.
The other side is 120 - 2x = 120 - 2*30 = 60 ft.
------------------------
Cheers,
Stan H.