Final answer:
The given side lengths of 5mm, 1mm, and 1mm do not satisfy the Triangle Inequality Theorem and cannot form a triangle, resulting in no triangle being possible with these dimensions.
Step-by-step explanation:
When determining whether a set of side lengths can form a unique triangle, we use the Triangle Inequality Theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the side lengths given are 5mm, 1mm, and 1mm.
To test this, we can add the lengths of any two sides and compare it to the third side:
- 1mm + 1mm = 2mm, which is not greater than 5mm
Since the sum of the lengths of the two shorter sides (1mm and 1mm) is not greater than the length of the longest side (5mm), these side lengths do not satisfy the Triangle Inequality Theorem. Therefore, they cannot form a triangle.
In conclusion, the given side lengths of 5mm, 1mm, and 1mm would not determine a unique triangle, multiple triangles, or any triangle at all. The side lengths would result in no triangle being formed.