triangles most basic property

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viny: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sat Jul 27, 2013 9:32 pm; Thanked: 2 times

by viny » Sun Aug 18, 2013 5:34 am

just a silly small question
sum of 2 sides of a triangle is > 3rd side
or
sum of 2 sides of a triangle is >= 3rd side

I checked a couple of websites I am finding both answers on the net which is the right 1.

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Source: Beat The GMAT — Problem Solving | Sun Aug 18, 2013 5:34 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 18, 2013 5:38 am

viny wrote:just a silly small question
sum of 2 sides of a triangle is > 3rd side
or
sum of 2 sides of a triangle is >= 3rd side

I checked a couple of websites I am finding both answers on the net which is the right 1.

It's a "strict" inequality. Here's the full rule:

If two sides of a triangle have lengths A and B, then |A-B| < third side < A+B

So, for example, if the two known sides have lengths 3 and 7, then |7-3| < third side < 7+3
Simplify to get: 4 < third side < 10

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Aug 18, 2013 12:36 pm

Hi viny,

This rule is called the Triangle Inequality Theorem and Brent has explained it well enough that I won't rehash it, but I can provide some background.

It's a rare geometry rule that you're more likely to see on Test Day if you're doing well in the Quant section (although you could do well and NOT see it, the Theorem can sometimes be "hidden" behind other concepts so you should keep your eyes open for it). You can actually use this rule to figure out maximum area or maximum perimeter of a triangle as well.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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tarik: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue May 21, 2013 10:22 am

by tarik » Mon Aug 19, 2013 2:32 pm

Thank you Brent for the complete rule.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Tue Aug 27, 2013 12:00 pm

Here's a handy way of remembering this rule. Think of constructing a triangle out of three sticks. One is 4cm, one is 5cm, and the other is unknown:

If we put the 4 and 5 end-to-end, they'd create a 9cm line, not a triangle. If we create a triangle, that 3rd side has to be less than 9 (less than the sum of the other two sides).

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Aug 27, 2013 11:28 pm

viny wrote:just a silly small question
sum of 2 sides of a triangle is > 3rd side
or
sum of 2 sides of a triangle is >= 3rd side

I checked a couple of websites I am finding both answers on the net which is the right 1.

If a and b are two sides of a triangle, where a - b > 0 and c is the third side, then the third side rule only states that a - b < c < a + b. That's it!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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