Triangle Inequality

Triangle Inequality

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

Example 1

Determine whether the given set of numbers can be the lengths of the sides of a triangle: 2, 3, 4.

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

Determine whether the given set of numbers can be the lengths of the sides of a triangle: 2, 7, 9.

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

Determine whether the given set of numbers can be the lengths of the sides of a triangle: 3, 4, 8.

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

Determine whether the given set of numbers can be the lengths of the sides of a triangle: 3, 5, 5.

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.