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Two sides of a (non-degenerate) triangle are 11 and 17. How many possible lengths are there for the third side, if it is a positive integer?

(pls show work)

 Jun 21, 2018
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By the Triangle Inequality, the sum of any two sides is greater than the remaining side

 

So we have these inequalities :

 

11 + n  > `17      subtract  11 from both sides

 

n  >  6

 

And

 

11 + 17  > n    

 

28 > n  ⇒    n < 28

 

So....combining these, we have

 

6 < n < 28

 

So......the number of possible integer lengths for the remaining side  =

 

[28  - 6]  - 1  = 

 

22 - 1  =  

 

21

 

cool cool cool

 Jun 21, 2018
edited by CPhill  Jun 21, 2018
edited by CPhill  Jun 21, 2018

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