Final answer:
Options A (11cm, 25cm, 14cm) and D (6cm, 10cm, 9cm) satisfy the Triangle Inequality Theorem and could represent the lengths of the sides of a triangle; option B (10cm, 4cm, 4cm) and the initial thought, option C (7cm, 7cm, 24cm), do not meet the conditions of the theorem.
Step-by-step explanation:
The question relates to determining the possible lengths of sides of a triangle.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
We will apply this theorem to the choices provided:
- A. 11cm, 25cm, 14cm: 11 + 14 > 25, 11 + 25 > 14, and 25 + 14 > 11. The inequality holds in all cases, so this set of lengths could form a triangle.
- B. 10cm, 4cm, 4cm: 10 + 4 > 4, but 4 + 4 is not > 10. This set of lengths cannot form a triangle.
- C. 7cm, 7cm, 24cm: 7 + 7 is not > 24. This set of lengths cannot form a triangle.
- D. 6cm, 10cm, 9cm: 6 + 10 > 9, 6 + 9 > 10, and 10 + 9 > 6. The inequality holds in all cases, so this set of lengths could form a triangle.
Based on the Triangle Inequality Theorem, the sets of lengths that could form a triangle are options A and D.