Question

Can a triangle be formed with the side lengths of 6.2 cm, 7.1 cm, and 15.1 cm?
A.
Since 6.2 cm + 7.1 cm < 15.1 cm, a triangle cannot be formed.

B.
Since 15.1 cm - 6.2 cm < 7.1 cm, a triangle cannot be formed.

C.
Since 6.2 cm + 7.1 cm < 15.1 cm, a triangle can be formed.

D.
Since 15.1 cm - 7.1 cm > 6.2 cm, a triangle can be formed.

Answer 1

To determine if a triangle can be formed with the side lengths of 6.2 cm, 7.1 cm, and 15.1 cm, we must apply the triangle inequality theorem. According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the conditions based on the provided side lengths:

1. **6.2 cm + 7.1 cm > 15.1 cm**:
- 6.2 + 7.1 = 13.3, which is not greater than 15.1. (Condition fails)

2. **6.2 cm + 15.1 cm > 7.1 cm**:
- 6.2 + 15.1 = 21.3, which is greater than 7.1. (Condition holds)

3. **7.1 cm + 15.1 cm > 6.2 cm**:
- 7.1 + 15.1 = 22.2, which is greater than 6.2. (Condition holds)

Since at least one of the conditions of the triangle inequality theorem is not satisfied (specifically, 6.2 + 7.1 < 15.1), a triangle cannot be formed with these lengths.

Therefore, the correct answer is:

**A. Since 6.2 cm + 7.1 cm < 15.1 cm, a triangle cannot be formed.**