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Two sides of a (non-degenerate) triangle are 21 and 29. How many possible lengths are there for the third side, if it is a positive integer?

 Jun 25, 2022
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By the triangle inequality

 

21 + x   >  29                           or                 21 + 29  >   x

 

x > 8                                                                x < 50

 

 

So  the possible lengths are

 

49 - 9 + 1  =   41

 

 

 

cool cool cool

 Jun 25, 2022

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