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)

Guest Jun 21, 2018

#1**+1 **

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

CPhill Jun 21, 2018