Results 1 to 5 of 5

Math Help - maximum area

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    112

    maximum area

    show that triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.(using calculus only)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    This may help you:

    Math Forum - Ask Dr. Math
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Quote Originally Posted by FernandoRevilla View Post
    This may help you:

    Math Forum - Ask Dr. Math
    Can someone check this(?):

     S_{ABC}=\frac{abc}{4R} is the area of triangle inscribed in a given circle of radius R.

     max\{S_{ABC}\}=max\{\frac{abc}{4R}\}

     max\{S_{ABC}\}=max\{\frac{a^3}{4R},\frac{b^3}{4R},  \frac{c^3}{4R} hence, [tex}a=b=c[/tex].
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2010
    Posts
    112
    let s=a+b+c where a,b,c are positive numbers .how can we prove that there sum is max. when they are equal.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2010
    Posts
    112
    Quote Originally Posted by ayushdadhwal View Post
    let s=a+b+c where a,b,c are positive numbers .how can we prove that there sum is max. when they are equal.
    can we generalize this result
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. maximum area
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 5th 2010, 07:16 PM
  2. Maximum Area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 3rd 2010, 04:52 PM
  3. Maximum Area
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 5th 2009, 07:25 PM
  4. Maximum possible area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 31st 2008, 09:12 PM
  5. Maximum Area
    Posted in the Calculus Forum
    Replies: 8
    Last Post: November 14th 2007, 01:01 AM

Search Tags


/mathhelpforum @mathhelpforum