Question 189349: A farmer has 500 feet of fencing to use to make a rectangular garden. One side of the garden will be a barn, which requires no fencing. How should the pen be built in order to enclose the largest amount of area possible?
Give your answer by filling in the blanks in the following sentence: The farmer should build the pen ______ feet away from the barn, and ________ feet wide, for an area of _______ square feet
How do I solve this?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A farmer has 500 feet of fencing to use to make a rectangular garden.
One side of the garden will be a barn, which requires no fencing.
How should the pen be built in order to enclose the largest amount of area possible?
:
Let L = the length
Let x = the width
:
We only need 3 sides so the perimeter equation would be:
L + 2x = 500
L = (500-2x)
:
Area = x * L
Substitute (500-2x) for L
A = x(500-2x)
A = -2x^2 + 500x
:
A quadratic equation, we can use the axis of symmetry and vertex to find the maximum area;
x = -500/(2*-2)
x = -500/-4
x = 125 ft is the width which will give max area
:
The length:
L = 500 - 2(125)
L = 250 ft is the length for max area
:
Find the max area
:
A = 250 * 125
A = 31,250 sq/ft
:
I'll let you fill in the blanks
"The farmer should build the pen ______ feet away from the barn, and ________
feet wide, for an area of _______ square feet
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