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Two side lengths of a triangle are 17 and 11. What is the longest possible integer length of the third side of the triangle?

 Jan 28, 2021
 #1
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29? I'm not sure. 

 Jan 28, 2021
 #2
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Not 29 or 30 ... 

 Jan 28, 2021
 #3
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the third side is 27

 Jan 28, 2021
 #4
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Let x be the third length of the triangle.

 

By triangle inequality, 

\(x < 17 + 11 \\ x < 28\)

 

The greatest integer solution of this inequality is \(x = 27\).

 

Therefore the longest possible third side is 27

 Jan 28, 2021

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