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To determine if the given side lengths \(10.7 \, \text{cm}\), \(3.2 \, \text{cm}\), and \(5.5 \, \text{cm}\) can form a triangle, we need to apply the **triangle inequality theorem**.

The triangle inequality theorem states that for any three sides to form a valid triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Specifically, for sides \(a\), \(b\), and \(c\) of a triangle, the following inequalities must hold:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Let’s check these conditions with the side lengths \(10.7 \, \text{cm}\), \(3.2 \, \text{cm}\), and \(5.5 \, \text{cm}\):

1. \( 10.7 + 3.2 = 13.9 \), and \( 13.9 > 5.5 \) (True)
2. \( 10.7 + 5.5 = 16.2 \), and \( 16.2 > 3.2 \) (True)
3. \( 3.2 + 5.5 = 8.7 \), and \( 8.7 < 10.7 \) (False)

Since the third inequality is not satisfied (\( 8.7 \) is not greater than \( 10.7 \)), these side lengths cannot form a triangle.

Thus, the correct answer is **B: No**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What happens when the triangle inequality theorem is violated?
2. How do you check if three angles can form a triangle?
3. Can you form a triangle with two sides equal and one different?
4. What are the different types of triangles based on side lengths?
5. How do we classify triangles based on their angles?

**Tip:** Always remember to verify the triangle inequality theorem when working with three given side lengths to determine if they form a valid triangle.

¿Pueden 10.7 cm, 3.2 cm y 5.5 cm ser las longitudes de los lados de un triángulo?

Explore whether side lengths of 10.7 cm, 3.2 cm, and 5.5 cm can form a triangle using the triangle inequality theorem. This geometry problem is suitable for students in Grades 6-9 and demonstrates a fundamental principle in determining the feasibility of triangle formation.

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