# 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:

### 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.

In the above triangle, following holds true:

*b* + *c* > *a*

*a* + *b* > *c*

*a* + *c* > *b*

*Example:***What is the possible range for x?**

So, the three inequalities for the above triangle are:

- (7 –
*x*) + 7 > 3*x*=> 14 –*x*> 3*x*=> 14 > 4*x*=>*x*=>*x*< - 3
*x*+ (7 –*x*) > 7 => 2*x*+ 7 > 7 => 2*x*> 0 =>*x*> 0 - 3
*x*+ 7 > 7 –*x =>*4*x*> 0 =>*x*> 0

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

**Check Point**

- Can the numbers 4, 5, 10 be the sides of a triangle?
- If 13 and 8 are the two sides of a triangle, then what is the possible range for the third side?
- Do the side lengths, 8, 11, and 16 form a triangle?
- If 3 + 2
*x*, 7 –*x*and 2*x*are the sides of a triangle, then what is the possible range for*x*? - If 10 and 15 are the two sides of a triangle, then what is the possible range for the third side?

##### Answer key

- No
- 5 <
*x*< 21 - Yes
- <
*x*< 10 - 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 | 21 Days | $114 |

1 session | 21 Days | $24 |

10 sessions | 2 months | $219 |

15 sessions | 3 months | $319 |

20 sessions | 3 months | $409 |

50 sessions | 6 months | $949 |

100 sessions | 10 months | $1849 |

## IN THE NEWS

Home

Summer Courses 2021

Tutoring

Test Prep

Worksheets

Pricing

About Us

Blog

Free Trial

Login

Terms of service

Privacy Policy

Money Back Guarantee

Technical requirements

FAQs

Job Opportunities

Sitemap

**Connect with us**

+1-269-763-4602

+1-269-763-5024

**Online test prep and practice**

SCAT

CogAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

©2021 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2021 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird