SOLUTION: A dog owner has 250 feet of fencing to enclose a rectangular run area for his dogs. If he wants the maximum possible area, what should the length and width of the rectangle be?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A dog owner has 250 feet of fencing to enclose a rectangular run area for his dogs. If he wants the maximum possible area, what should the length and width of the rectangle be?      Log On


   

Question 1112769: A dog owner has 250 feet of fencing to enclose a rectangular run area for his dogs. If he wants the maximum possible area, what should the length and width of the rectangle be?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer.  The maximum possible area is  %28250%2F4%29%5E2 = 3906.25 sq. ft.

Solution

A rectangle with a given perimeter which has the maximal area is a square.


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For detailed proof and explanation see the lesson in the list below marked (*).

On finding the maximum/minimum of a quadratic function and relevant issues see my lessons
    - 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
    - Using quadratic functions to solve problems on maximizing revenue/profit
    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function

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

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


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.