Final answer:
The side lengths of 10.6 cm, 5.6 cm, and 4.0 cm cannot form a triangle because their sum does not satisfy the triangle inequality theorem.
Step-by-step explanation:
The question is whether the side lengths of 10.6 cm, 5.6 cm, and 4.0 cm can form a triangle. To determine this, we can use the triangle inequality theorem, which 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 this particular case, we check if:
- 10.6 cm + 5.6 cm > 4.0 cm
- 10.6 cm + 4.0 cm > 5.6 cm
- 5.6 cm + 4.0 cm > 10.6 cm
Adding the lengths of the two smaller sides, 5.6 cm and 4.0 cm, gives us 9.6 cm, which is not greater than the length of the longest side, 10.6 cm. Therefore, the sides do not satisfy the triangle inequality theorem, and these side lengths cannot form a triangle. Hence, the answer to the question is No.