Final answer:
To determine if the given sets of side lengths can form a triangle, we apply the triangle inequality theorem to each. Only the sets that satisfy the inequality for all pairs of sides can form a triangle. The provided examples show this step-by-step evaluation.
Step-by-step explanation:
The question involves determining whether sets of side lengths can form a triangle. This can be tested using the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. We must check if each pair of side lengths added together is greater than the third side for the given sets. Let's break it down step by step for each set:
- For the set 11.5, 10.5, 6.1: 11.5 + 10.5 > 6.1 (Yes), 11.5 + 6.1 > 10.5 (Yes), and 10.5 + 6.1 > 11.5 (Yes) - therefore, these can form a triangle.
- For the set 9.5, 3.5, 4.5: 9.5 + 3.5 > 4.5 (Yes), 9.5 + 4.5 > 3.5 (Yes), and 3.5 + 4.5 > 9.5 (No) - these cannot form a triangle.
- For the set 8, 6.7, 1: 8 + 6.7 > 1 (Yes), 8 + 1 > 6.7 (Yes), and 6.7 + 1 > 8 (No) - these cannot form a triangle.
- For the set 8, 6.7, 9.8: 8 + 6.7 > 9.8 (Yes), 8 + 9.8 > 6.7 (Yes), and 6.7 + 9.8 > 8 (Yes) - therefore, these can form a triangle.
- For the set 5, 6, 8: 5 + 6 > 8 (Yes), 5 + 8 > 6 (Yes), and 6 + 8 > 5 (Yes) - therefore, these can form a triangle.
- For the set 9.5, 7.5, 8.5: 9.5 + 7.5 > 8.5 (Yes), 9.5 + 8.5 > 7.5 (Yes), and 7.5 + 8.5 > 9.5 (Yes) - therefore, these can form a triangle.