For instance, can I create a triangle from sides of length...say 4, 8 and 3?

No!It's actually not possible!

As you can see in the picture below, it's not possible to create a triangle that has side lengths of
4, 8, and 3

It turns out that there are some rules about the
side lengths of triangles.
You can't just make up 3 random numbers and have a
triangle! You could end up with 3 lines like those pictured above that
cannot be connected to form a triangle.

Video On Theorem

The Formula

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the
measure of the third side.

Note: This rule must be satisfied for all 3 conditions of the sides.

In other words, as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side,
then you know that the sides do not make up a
triangle.

The interactive demonstration below shows that the sum of the lengths of any 2 sides of a triangle must
exceed the length of the third side. The demonstration also illustrates what happens when the sum of 1 pair of sides
equals the length of the third side--you end up with a straight line! You can't make a triangle!

Otherwise, you cannot create a triangle
from the 3 sides.

Demonstration 1

When the sum of 1 pair of sides exactly equals the measure of a 3^{rd} side.

Demonstration 2

When the sum of 1 pair of sides is less than the measure of a 3^{rd} side.

Content on this page requires a newer version of Adobe Flash Player.

Use the triangle inequality theorem
and examine all 3 combinations of the sides. As soon as the sum of any 2 sides is less than the third side
then the triangle's sides do not satisfy the theorem.