To determine how many triangles can be formed with given side lengths, we can use the triangle inequality theorem, which states that for any three sides \( a \), \( b \), and \( c \), the following inequalities must hold true:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
If all three inequalities are satisfied, then exactly one unique triangle can be formed with those side lengths.
If any of the inequalities fail, then no triangle can exist with the given sides.
If \( a = b = c \) (all sides equal), there is also just one unique triangle; however, if any two sides are equal and the third is different, you can still form a triangle but it would also be unique.
To determine the nature of the triangle or whether it exists, you'll need specific side lengths to evaluate this theorem. Please provide the side lengths to further analyze the situation.