Question

in the three segments form a triangle
24
16
44

Answer 1

To determine whether three segments can form a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle formed by segments of lengths \(a\), \(b\), and \(c\), the following must hold true:

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

Let's denote the segments as follows:
- \(a = 24\)
- \(b = 16\)
- \(c = 44\)

Now we will check the inequalities:

1. \(24 + 16 > 44\)
\(40 > 44\) (This is false)

2. \(24 + 44 > 16\)
\(68 > 16\) (This is true)

3. \(16 + 44 > 24\)
\(60 > 24\) (This is true)

Since the first inequality is false, the segments of lengths 24, 16, and 44 cannot form a triangle.