Select Page

# Triangle Inequality Theorem

The sum any two sides in a triangle is always greater than the third side of triangle.

If one side is longer than the sum of other two sides as shown below, then it is not a triangle.

See the example below:

In the above case, AD + BC = 18 + 9 = 27 units, which is less than side AB of length 30 units. Here since one side AB is longer, so the other two sides, AD and BC don’t meet.

In the above triangle, following holds true:

b + c > a

a + b > c

a + c > b

Example: What is the possible range for x?

According to Triangle Inequality Theorem, the sum any two sides in a triangle is always greater than the third side of triangle.

So, the three inequalities for the above triangle are:

1. (7 – x) + 7 > 3x => 14 – x > 3x => 14 > 4x => x =>x <
2. 3x + (7 – x) > 7 => 2x + 7 > 7 => 2x > 0 => x > 0
3. 3x + 7 > 7 – x => 4x > 0 => x > 0

Combining the three inequalities, we get the possible range as 0 < x <

#### Check Point

1. Can the numbers 4, 5, 10 be the sides of a triangle?
2. If 13 and 8 are the two sides of a triangle, then what is the possible range for the third side?
3. Do the side lengths, 8, 11, and 16 form a triangle?
4. If 3 + 2x, 7 – x and 2x are the sides of a triangle, then what is the possible range for x?
5. If 10 and 15 are the two sides of a triangle, then what is the possible range for the third side?
1. No
2. 5 < x < 21
3. Yes
4. < x < 10
5. 5 < x < 25

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?