Final answer:
Option B: 4, 8, 12 cm could not form a triangle, as the sum of the two shorter sides is not greater than the length of the longest side, violating the triangle inequality theorem.
Step-by-step explanation:
When determining if three lengths can form a triangle, there is a simple rule that needs to be followed known as 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 for those lengths to be able to form a triangle.
- Option A: 8, 13, 7 cm can form a triangle since the sum of any two sides is greater than the third (e.g., 8+7 > 13, 8+13 > 7, 13+7 > 8).
- Option B: 4, 8, 12 cm cannot form a triangle since 4 + 8 is not greater than 12.
- Option C: 17, 9, 9 cm can form a triangle since the sum of the two shorter sides is greater than the length of the longest side (9+9 > 17).
- Option D: 5, 6, 7 cm can form a triangle since the sum of any two sides is greater than the third (5+6 > 7, 5+7 > 6, 6+7 > 5).
Hence, the set of lengths that could not form a triangle from the options provided is Option B: 4, 8, 12 cm.