# Triangle Inequality

How to solve triangle inequality theorem problems: examples and their solutions.

## Example 1

shorter sides: 2, 3

longest side: 4

2 + 3 > 4 is true.

So 3, 4, and 5 can be the sides of a triangle.

## Example 2

shorter sides: 2, 7

longest side: 9

2 + 7 > 9 is false.

So 2, 7, and 9 cannot be the sides a triangle.

## Example 3

shorter sides: 3, 4

longest side: 8

3 + 4 > 8 is false.

So 3, 4, and 8 cannot be the sides of a triangle.

## Example 4

If there are two or three longest side,

then just consider one of them as the longest side.

shorter sides: 2, 5

longest side: 5

3 + 5 > 5 is true.

So 3, 5, and 5 can be the sides of a triangle.