SOLUTION: Solve. We are working with Quadratic Equations and Functions You have 188 ft of fencing to enclose a rectangular region. What is the maximum area?

Question 84576: Solve. We are working with Quadratic Equations and Functions
You have 188 ft of fencing to enclose a rectangular region. What is the maximum area?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve. We are working with Quadratic Equations and Functions:
:
You have 188 ft of fencing to enclose a rectangular region. What is the maximum area?
Perimeter:
2L + 2W = 188
Simplify, divide equation by 2:
L + W = 94
W = 94 - L
:
Let x = length
Then:
(94-x) = width
:
The area = y:
y = x(94-x)
y = -x^2 + 94x; a quadratic equation:
:
Find the axis of symmetry: x = -b/(2a)
In our equation: a = -1; b = +94
x = -94/(2*-1)
x = -94/-2
x = +47 the axis of symmetry
:'
Substitute 47 for x in the equation to find the vertex (max)
y = -(47^2) + 94(47)
y = -2209 + 4418
y = +2209 sq/ft max area with 188 ft perimeter

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