Explanation:

To determine if these options can be sides of a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the third side.

- Option 1: 12 cm, 9 cm, and 15 cm

- 12 + 9 > 15

- 12 + 15 > 9

- 9 + 15 > 12

- All conditions are satisfied.

- Option 2: 20 cm, 20 cm, and 20 cm

- Each pair of sides adds up to more than the third.

- A classic equilateral triangle.

- Option 3: 3 cm, 5 cm, and 4 cm

- 3 + 5 > 4

- 3 + 4 > 5

- 5 + 4 > 3

- All conditions are satisfied.

- Option 4: 3 cm, 5 cm, and 1 cm

- 3 + 5 > 1

- 3 + 1 is not > 5

- Does not satisfy all conditions.

Option 4 cannot be sides of a triangle.

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