Question

Given three side lengths, how many triangles can be formed?

Answer 1

Given three side lengths, for example, a, b and c, you can form the triangle when

$a+b>c,\\ a+c>b,\\ b+c>a.$

If this property holds, then one triangle you can form. Each next triangle with the same sides lengths will be congruent to the first triangle by SSS postulate.

SSS postulate says: If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Answer: 1 triangle, correct option is A.

Answer 2

We know that

In a triangle, the combined lengths of any two sides must always be greater than the length of the third side. (Triangle Inequality Theorem)

If all three side lengths are given and the combined length of two sides is greater than the length of the third side.

then 

 one unique triangle can be made