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Math Help - Triangles - Greatest Area

  1. #1
    Senior Member DivideBy0's Avatar
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    Triangles - Greatest Area

    I have 5 triangles, which have sides 3-4-2, 3-4-3, 3-4-4, 3-4-5, 3-4-6. Is there a way to tell which has the largest area without using lengthy formulae? Thanks.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    I have 5 triangles, which have sides 3-4-2, 3-4-3, 3-4-4, 3-4-5, 3-4-6. Is there a way to tell which has the largest area without using lengthy formulae? Thanks.
    That depends on what you mean by "lengthy."

    A = sqrt{s*(s - a)*(s - b)*(s - c)}
    where s = (a + b + c)/2

    isn't all that long to do.

    -Dan
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  3. #3
    Senior Member DivideBy0's Avatar
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    Lol, well thanks for that, but is there a general kind of rule of thumb you can use to determind which triangle is larger at a glance?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    Lol, well thanks for that, but is there a general kind of rule of thumb you can use to determind which triangle is larger at a glance?
    Probably only if they are drawn out for you.

    -Dan
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  5. #5
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    Hello, DivideBy0!

    I have 5 triangles, which have sides 3-4-2, 3-4-3, 3-4-4, 3-4-5, 3-4-6.
    Is there a way to tell which has the largest area without using lengthy formulae? .Yes!

    The area of a triangle is: .A .= .bh

    Make sketches of the triangles, using 4 as the base.
    Code:
                                              *
                 3    *                  3  * : *  3
                  *   :* 2                *   :   *
              *       : *               *     :     *
          *  *  *  *  *  *            *   *   *   *   *
                  4                           4
    
    
                                      *
              *                       *  *   5
           3 *: *                   3 *     *
            * :   * 4                 *        *
           *  :     *                 *           *
          *   *   *   *               *   *   *   *   *
                4                              4
    
          *
          :*  *    6
          :3*     *
          :  *        *
          .   *   *   *   *
                    4

    They all have a base of 4.

    Which triangle has the greatest height?

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