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Lagrange multipliers and triangles

  1. Apr 4, 2005 #1
    Use Lagrange Multipliers to prove that the triangle with the maximum area that has a given perimeter p is equilateral.
    [Hint: Use Heron’s formula for the area of a triangle: A = sqrt[s(s - x)(s - y)(s - z)] where s = p/2 and x, y, and z are the lengths of the sides.]

    I have no idea how to do this.
     
  2. jcsd
  3. Apr 4, 2005 #2

    dextercioby

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    U have a function of 3 varibles (the area) and a constraint depending on these 3 variables (the perimeter is constant).So basically construct the constaint "area" function and then apply the theory...

    Daniel.
     
  4. Apr 4, 2005 #3

    HallsofIvy

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    Are you saying that you don't know what "Lagrange multipliers" are?

    The problem is to maximize [tex]A= \sqrt{s(s-x)(s-y)(s-z)}[/tex] subject to the condition x+ y+ z= p.

    One nice thing about "Lagrange multipliers" is that we can find important information
    (like x= y= z) without having to find x, y, z specifically- eliminate the "multiplier" [tex] \lambda [/tex] from the equations and see what happens.
     
    Last edited: Apr 6, 2005
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