How many (non-congruent) isosceles triangles exist which have a perimeter of 10 and integer side lengths?
2 - 2 - 6 triangle does not work, because 2 + 2 is less than 6.
Thus, the only working options are 3 - 3 - 4 and 2 - 4- 4, making \(\color{brown}\boxed{2}\) options.