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In a triangle with side lengths 5, 6 and x, what is the sum of all possible integral values of x?

AdminMod2  Aug 11, 2017
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 According to  the Triangle Inequality, we have the following

 

5 + 6 > x     →  x < 11      

6 + x > 5     →  x > - 1

5 + x > 6     →  x > 1

 

Choosing the most restrictive solution interval.....

 

2  ≤ x  ≤ 10

 

Therefore.....x  =   { 2, 3, 4, 5 ,6 ,7 , 8, 9, 10 }

 

And the sum  of these values  = 54

 

 

cool cool cool

CPhill  Aug 11, 2017

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