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Two sides of a (non-degenerate) triangle are 21 and 27. How many possible lengths are there for the third side, if it is a positive integer?

 Dec 2, 2020
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This has to satisfy the triangle inequality  that says that the  sum of any two side lengths of a triangle are greater than the remaining side

 

So...let x be the possible unlnown side lengths.....and we have that

 

21 + 27  >  x               and           21 + x  >  27

48 > x                                                x > 6

 

 

So....the possible side lengths  are  [ 7 , 47 ]

 

The number of positive integers =  47 - 7  + 1 =   41

 

 

cool cool cool

 Dec 2, 2020

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