Related Content

Thank you!

On behalf of our dedicated team, we thank you for your continued support. It's fulfilling to see so many people using Voovers to find solutions to their problems. Thanks again and we look forward to continue helping you along your journey!

Nikkolas and Alex
Founders and Owners of Voovers

Triangle Inequality Theorem

What is the Triangle Inequality Theorem?

The triangle inequality theorem tells us that:
The sum of two sides of a triangle must be greater than the third side.
This theorem can be used to prove if a combination of three triangle side lengths is possible. See the image below for an illustration of the triangle inequality theorem.

triangle inequality theorem

Example Problem

Referencing sides x, y, and z in the image above, use the triangle inequality theorem to eliminate impossible triangle side length combinations from the following list.
1.) x = 2, y = 3, z = 5
2.) x = 5, y = 12, z = 13
3.) x = 3, y = 4, z = 5
4.) x = 12, y = 13, z = 27
5.) x = 2, y = 9, z = 12

Side length combinations #1, #4, and #5 do not satisfy the requirements of the triangle inequality theorem and therefore are not possible.

Scroll to Top