Thread: 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.

Originally Posted by 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? 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

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?

Originally Posted by DivideBy0

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

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 .= .½·b·h

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?