Two side lengths of a triangle are 17 and 11. What is the longest possible integer length of the third side of the triangle?

29? I'm not sure.

Not 29 or 30 ...

the third side is 27

Let x be the third length of the triangle.

By triangle inequality,

\(x < 17 + 11 \\ x < 28\)

The greatest integer solution of this inequality is \(x = 27\).

Therefore the longest possible third side is 27