SOLUTION: You have 200 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will ma

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: You have 200 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will ma      Log On


   

Question 794816: You have 200 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
Quadratic functions
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Width = x feet
Length = 200 - 2x
Area = x(200 - 2x)
Area(x)= 200x - 2x^2
Area'(x) = 200 - 4x
A(x) = 0
200 - 4x = 0
-4x = -200
x = 50
Using Nature Table:
................ - 50 +
200 - 4x... + 0 -
So, x = 50 feet is a maximum.
Width = 50 feet
Length = 100 feet
Area = 50*100 = 5000 feet.
Hope this helps.
:-)