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triangles most basic property

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triangles most basic property

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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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

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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.

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by tarik » Mon Aug 19, 2013 2:32 pm
Thank you Brent for the complete rule.
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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).

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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!
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