Final answer:
By applying the triangle inequality theorem, which requires the sum of any two sides of a triangle to be greater than the third, it's determined that a triangle with side lengths of 2.7, 3.1, and 4.3 can indeed be formed because all conditions of the theorem are satisfied.
Step-by-step explanation:
To determine if a triangle can be formed with the side lengths of 2.7, 3.1, and 4.3, we can use the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Here's how we can apply it to our case:
- First side + Second side > Third side: 2.7 + 3.1 > 4.3?
- Second side + Third side > First side: 3.1 + 4.3 > 2.7?
- First side + Third side > Second side: 2.7 + 4.3 > 3.1?
When we add the side lengths together, we find:
- 2.7 + 3.1 = 5.8, which is greater than 4.3
- 3.1 + 4.3 = 7.4, which is greater than 2.7
- 2.7 + 4.3 = 7.0, which is greater than 3.1
Since all three conditions are satisfied, a triangle with the given side lengths is possible.