Question 996435
If you mean that the sides of the triangle can be real numbers (decimals or fractions), then there are an infinite number of triangles that can be constructed.
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If you mean that the sides of the triangle are whole numbers, then there is a limited number of possible triangles. We are looking for solutions that solve
a + b + c = 12
The triangle inequality says that the sum of any two sides of a triangle must be greater than the third.  Therefore, we can write down the possibilities
1) 2 - 5 - 5
2) 3 - 5 - 4
3) 4 - 4 - 4
4) 5 - 4 - 3
5) 5 - 5 - 2
There are 5 possibilities