A triangle can be constructed by taking its sides as:

Options

A. 1.8 cm, 2.6 cm, 4.4 cm
B. 2 cm, 3 cm, 4 cm
C. 2.4 cm, 2.4 cm, 6.4 cm
D. 3.2 cm, 2.3 cm, 5.5 cm

Answer

To determine whether a triangle can be constructed with given side lengths, we need to apply the triangle inequality theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold true:

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

Let's analyze the options step by step.

### Step-by-Step Solution:

**Option 1: 1.8, 2.6, and 4.4**

1. Check \(1.8 + 2.6 > 4.4\):
- \(1.8 + 2.6 = 4.4\) (not greater, equal)

Since this condition is not satisfied, we cannot form a triangle with these sides.

**Option 2: 2, 3, and 4**

1. Check \(2 + 3 > 4\):
- \(2 + 3 = 5 > 4\) (satisfied)

2. Check \(2 + 4 > 3\):
- \(2 + 4 = 6 > 3\) (satisfied)

3. Check \(3 + 4 > 2\):
- \(3 + 4 = 7 > 2\) (satisfied)

Since all conditions are satisfied, we can form a triangle with these sides.

**Option 3: 2.4, 2.4, and 6.4**

1. Check \(2.4 + 2.4 > 6.4\):
- \(2.4 + 2.4 = 4.8 < 6.4\) (not satisfied)

Since this condition is not satisfied, we cannot form a triangle with these sides.

**Option 4: 3.2, 2.3, and 5.5**

1. Check \(3.2 + 2.3 > 5.5\):
- \(3.2 + 2.3 = 5.5\) (not greater, equal)

Since this condition is not satisfied, we cannot form a triangle with these sides.

### Conclusion:
The only option that satisfies the triangle inequality theorem is **Option 2: 2, 3, and 4**.