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)
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