Final answer:
A triangle cannot be formed with side lengths 12.3, 13.9, and 25.2 because they do not satisfy the Triangle Inequality Theorem, which requires the sum of any two sides to be greater than the third side.
Step-by-step explanation:
To determine whether it is possible to form a triangle with side lengths 12.3, 13.9, and 25.2, we can use the Triangle Inequality Theorem. This 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. Here, we check if 12.3 + 13.9 > 25.2. When we add 12.3 and 13.9, we get 26.2, which is indeed greater than 25.2, so this condition is met.
However, we must check all combinations of sides:
- 12.3 + 25.2 = 37.5, which is greater than 13.9.
- 13.9 + 25.2 = 39.1, which is greater than 12.3.
While the first and second conditions are met, the third condition fails because 12.3 + 13.9 is not greater than the longest side, 25.2. Therefore, according to the Triangle Inequality Theorem, a triangle with these side lengths cannot be formed because one condition fails to satisfy the theorem.