Question

Can a triangle be formed with the side lengths of 6.9 cm, 7.6 cm, and 16 cm?
A.
Since 16 cm - 7.6 cm > 6.9 cm, a triangle can be formed.

B.
Since 6.9 cm + 7.6 cm < 16 cm, a triangle can be formed.

C.
Since 6.9 cm + 7.6 cm < 16 cm, a triangle cannot be formed.

D.
Since 16 cm - 6.9 cm < 7.6 cm, a triangle cannot be formed.

Answer 1

To determine whether a triangle can be formed with the side lengths of 6.9 cm, 7.6 cm, and 16 cm, we can use the triangle inequality theorem. The theorem states that for any triangle with sides \(a\), \(b\), and \(c\), the following conditions must be met:

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

Let's apply this theorem to the given side lengths:

1. **6.9 cm + 7.6 cm > 16 cm**
\(6.9 + 7.6 = 14.5\) which is **not greater** than 16.

2. **6.9 cm + 16 cm > 7.6 cm**
\(6.9 + 16 = 22.9\) which is greater than 7.6.

3. **7.6 cm + 16 cm > 6.9 cm**
\(7.6 + 16 = 23.6\) which is greater than 6.9.

Since the first condition \(6.9 + 7.6 > 16\) does not hold true, the three side lengths cannot form a triangle.

Thus, the correct conclusion is:

C. Since \(6.9 \, \text{cm} + 7.6 \, \text{cm} < 16 \, \text{cm}\), a triangle cannot be formed.