Final answer:
Using the Triangle Inequality Theorem, only Option C (3 cm, 4 cm, 5 cm) satisfies the condition that the sum of any two sides must be greater than the third side, hence can form a triangle.
Step-by-step explanation:
To determine which set of side lengths can form a triangle, we can use 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. Let's apply this theorem to each set of given side lengths:
- A. 2 cm, 2 cm, 4 cm: Here, 2 + 2 is not greater than 4, so these side lengths cannot form a triangle.
- B. 3 cm, 5 cm, 10 cm: Similarly, 3 + 5 is not greater than 10, so these side lengths cannot form a triangle either.
- C. 3 cm, 4 cm, 5 cm: In this case, 3 + 4 is greater than 5, 3 + 5 is greater than 4, and 4 + 5 is greater than 3. Hence, these side lengths do satisfy the Triangle Inequality Theorem and can form a triangle.
- D. 4 cm, 8 cm, 15 cm: Here, 4 + 8 is less than 15, so these side lengths cannot form a triangle.
The only set of side lengths that can form a triangle is Option C: 3 cm, 4 cm, and 5 cm.