You can put this solution on YOUR website! 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
