# Thread: Triangles - Greatest Area

1. ## 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.

2. 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

3. 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?

4. 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

5. 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?