Lengths Can be side lengths of a triangle
14, 3, 4 No
18.2, 5.2, 12.1 Yes
5, 15, 13 Yes
8, 21, 3 No
Here's the analysis for each set of lengths:
1. 14, 3, 4:
Check the Triangle Inequality Theorem:
14 + 3 > 4 (true)
14 + 4 > 3 (true)
3 + 4 > 14 (false)
Therefore, this set of lengths cannot be the side lengths of a triangle.
2. 18.2, 5.2, 12.1:
Check the Triangle Inequality Theorem:
18.2 + 5.2 > 12.1 (true)
18.2 + 12.1 > 5.2 (true)
5.2 + 12.1 > 18.2 (true)
Therefore, this set of lengths can be the side lengths of a triangle.
3. 5, 15, 13:
Check the Triangle Inequality Theorem:
5 + 15 > 13 (true)
5 + 13 > 15 (true)
15 + 13 > 5 (true)
Therefore, this set of lengths can be the side lengths of a triangle.
4. 8, 21, 3:
Check the Triangle Inequality Theorem:
8 + 21 > 3 (true)
8 + 3 > 21 (false)
21 + 3 > 8 (true)
Therefore, this set of lengths cannot be the side lengths of a triangle.