Posted by Knights on .
Two sides of a triangle are 11 and 17. How many possible lengths are there for the third side, if it is a positive integer?
I tried listing them all but I get confused...Please help thank you!

math problem triangle inequality help 
Reiny,
The sum of any two sides must be greater than the third side for a triangle to exist
let the third side be x
x+11>17 AND x+17>11 AND 11+17> x
x > 6 AND x>6 AND x < 28
so 6 < x < 28
So how many positive integers can you count between 6 and 28 exclusive ? 
math problem triangle inequality help 
Art od Problem Solving,
PLEASE DO NOT TRY TO CHEAT AND USE THE INTERNET FOR YOUR ANSWERS TO YOUR HOMEWORK THANKS!
Let the third side be $n$. Then by the triangle inequality,
\begin{align*} n + 11 &> 17, \\ n + 17 &> 11, \\ 11 + 17 &> n, \end{align*}
which gives us the inequalities $n > 6$, $n > 6$, and $n < 28$. Therefore, the possible values of $n$ are 7, 8, $\dots$, 27, for a total of $27  7 + 1 = \boxed{21}$ possible values.