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

Guest Jun 27, 2018

#2**+1 **

5 , 6 and x

By the triangle inequality, we have two situations

We have that

5 + 6 > x

11 > x

So x < 11

And

5 + x > 6

x > 1

So...we have the following dual inequality

1 < x < 11

So....the possible integer values for x are 2,3,4,5,6,7,8,9,10

And the sum of these is just (10) (11) / 2 - 1 = 55 - 1 = 54

CPhill Jun 27, 2018