Which one of the following combinations of measurements can form the sides of a triangle?
11 cm, 3 cm, 6 cm
To determine if a given set of measurements can form the sides of a triangle, the Triangle Inequality Theorem must be satisfied. 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. Let's analyze each option:
- Option 1 (9 cm, 6 cm, 2 cm): 9 + 6 > 2 (True), 9 + 2 > 6 (True), but 6 + 2 = 8 < 9 (False). This combination cannot form a triangle.
- Option 2 (11 cm, 3 cm, 6 cm): 11 + 3 > 6 (True), 11 + 6 > 3 (True), 3 + 6 = 9 > 11 (False). This combination can form a triangle.
- Option 3 (3 cm, 5 cm, 8 cm): 3 + 5 = 8 (False). This combination cannot form a triangle.
- Option 4 (5 cm, 7 cm, 13 cm): 5 + 7 = 12 < 13 (False). This combination cannot form a triangle.
Therefore, only the combination 11 cm, 3 cm, and 6 cm satisfies the Triangle Inequality Theorem and can form the sides of a triangle.
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