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Find the dimensions of the rectangle

  1. Nov 14, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.


    2. Relevant equations

    (x-a)^2 + (y-b)^2 = r^2
    max area = 2x(2y)
    = 4xy
    3. The attempt at a solution

    (x-a)^2 + (y-b)^2 = r^2
    = y=r-(x-a)+b

    I then plug this into the max area
    = 4x(r-(x-a)+b)

    I know I need to differentiate, but I'm not sure how to go about this. I know I need to use the product rule, if its setup properly.
     
  2. jcsd
  3. Nov 14, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Optimization

    How in the world did you get this? Surely not by taking the square root of both sides!

    No, it not at all set up properly!
     
  4. Nov 14, 2008 #3
    Re: Optimization

    Ok wow I can't believe I did that.

    So I FOIL it out and get this

    x^2 = r^2 + 2ax - a^2 - y^2 + 2by - b^2

    x= r-a-b+sqrt(2ax)+sqrt(2by)

    Does this look better?
     
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