Math help needed: which set of lengths could represent the sides of a triangle?

label Mathematics
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7,8,14

3,7,10

6,7,14

4,6,10

Dec 14th, 2015

Hello!

The lengths of a triangle's sides a, b, c must satisfy c<a+b, a<b+c, b<c+a,
and this is also a sufficient condition.

The first: 14<7+8, 7<8+14 and 8<7+14 are all true. YES

The second: 10<3+7 is false. NO

The third: 14<6+7 is false. NO

The fourth: 10<4+6 is false. NO

The answer: the first set only.

Please ask if something is unclear.
Dec 14th, 2015

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Dec 14th, 2015
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Dec 14th, 2015
Jun 23rd, 2017
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