Select Page

Triangle Inequality Theorem

Grade 7 Math Worksheets

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:

triangle inequality theorem

Schedule a Free session to clear worksheet doubts

No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!

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.

triangle inequality theorem

In the above triangle, following holds true:

b + c > a

a + b > c

a + c > b

Example: What is the possible range for x?

triangle inequality theorem
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 =>\frac{7}{2} x =>x <\frac{7}{2}
  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 <\frac{7}{2}

 

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?
Answer key
  1. No
  2. 5 < x < 21
  3. Yes
  4. \frac{4}{5}< x < 10
  5. 5 < x < 25

Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE Demo Session.

No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!

Pricing for Personalized Online Tutoring

Tutoring Package Validity Grade (1-12), College
5 sessions 1 Month $119
1 session 1 Month $24
10 sessions 3 months $229
15 sessions 3 months $339
20 sessions 4 months $429
50 sessions 6 months $999
100 sessions 12 months $1949

Give your child an academic boost this fall

 

10% discount on all Learning Packs

Use coupon FALL10

Valid till September 30, 2021

You have Successfully Subscribed!