SOLUTION: There are cartons full of fencing. Each carton has 24 ft of fencing inside. If Amy wants to have a rectangular garden with the largest area possible what is the area

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: There are cartons full of fencing. Each carton has 24 ft of fencing inside. If Amy wants to have a rectangular garden with the largest area possible what is the area      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 975411: There are cartons full of fencing. Each carton has 24 ft of fencing inside. If Amy wants to have a rectangular garden with the largest area possible what is the area
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rectangle has l and w
l*w is a maximum
l*(24-l) is maximum
24l -l^2 is maximum when?
-l^2+24l=y
x=-b/2a = -24/-2=12
The rectangle with maximum area is a square with length and width 12. The area is 144 sq ft.
graph%28300%2C200%2C-15%2C15%2C-15%2C200%2C-x%5E2%2B24x%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There are cartons full of fencing. Each carton has 24 ft of fencing inside. If Amy wants to have a rectangular garden with the largest area possible what
is the area?
-----------------------
Area = length*width
A = x(24-x) = 24x-x^2
-------
A'(x) = 24-2x
------
Solve:: 24-2x = 0
x = 12
24-x = 12
----
Ans: Both width and length are 12'
The rectangle is a square.
--------
Cheers,
Stan H.
-----------