SOLUTION: a farmer is fencing a rectangular area for cattle and use the straight portion of a river as one side of the rectangle, note that there is no fence along the river. if the farmer h

Algebra ->  Rectangles -> SOLUTION: a farmer is fencing a rectangular area for cattle and use the straight portion of a river as one side of the rectangle, note that there is no fence along the river. if the farmer h      Log On


   

Question 1058112: a farmer is fencing a rectangular area for cattle and use the straight portion of a river as one side of the rectangle, note that there is no fence along the river. if the farmer has 2500 feet of fence find the dimensions for the rectangular area that gives the maximum area for the cattle
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a farmer is fencing a rectangular area for cattle and use the straight portion of a river as one side of the rectangle, note that there is no fence along the river. if the farmer has 2500 feet of fence find the dimensions for the rectangular area that gives the maximum area for the cattle
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Sketch a rectangle with the river as the back side
width + 2(height) = 2500
Area = width*height
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A = (2500-2h)h
A = 2500h - 2h^2
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Max Area occurs when h = -b/(2a) = -2500/(-4) = 625 ft.
Solve for "width"
width = 2500 - 2(625) = 1250 ft.
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Cheers,
Stan H.
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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
See the lesson
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
in this site.

Very similar problem was solved there specially for you with detailed explanations.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

Other lessons under this topic are
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area