A student has sticks of lengths 5 cm and 9 cm. She wants to use a third stick to form a triangle. What are the possible lengths of the third side?
We can use the triangle inequality to solve this
n < 5 + 9 n + 5 > 9
n < 14 n > 4
So the possible lengths, n, for the third side are
4 < n < 14
If we want integer lengths we get n = 5,6,7,8,9,10,11,12,13