SOLUTION: We want to bbuild a pen out of 600 meters of fence. It is to be rectangular and divided into two congruent sections. What dimensions will give us the largest possible area? I

Question 140289: We want to bbuild a pen out of 600 meters of fence. It is to be rectangular and divided into two congruent sections. What dimensions will give us the largest possible area?
I am lost. Do I have to use the derivative?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
We want to build a pen out of 600 meters of fence. It is to be rectangular and divided into two congruent sections. What dimensions will give us the largest possible area?
:
Write a quadratic equation and find the axis of symmetry:
:
Let x = width
Let L = length
:
Using the perimeter equation (3 widths, to include the dividing fence):
2L + 3x = 600
2L = 600 - 3x
L = (300 - 1.5x); divided by 2
:
Area = L * x
Substitute (300-1.5x) for x
A = x(300-1.5x)
A = -1.5x^2 + 300x; a quadratic equation
:
Use the axis of symmetry formula: x = -b/(2a)
a=-1,5; b = +300
:
x =
x =
x = +100 m is the width for max area
:
We know L = (300-1.5x)
L = 300 - 1.5(100)
L = +150 m is the length
:
:
Check in the perimeter: 2(150) + 3(100) = 600
:
max Area = 150 * 100 = 15,000 sq/m

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