Question

Can the three segments form a triangle
30
60
28

Answer 1

To determine if three segments can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three sides \(a\), \(b\), and \(c\) of a triangle, the following conditions must hold:

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

In this case, we have the segments with lengths 30, 60, and 28. Let's denote these lengths as follows:
- \(a = 30\)
- \(b = 60\)
- \(c = 28\)

Now we will check the triangle inequalities:

1. \(a + b > c\):
\(30 + 60 > 28\)
\(90 > 28\) (True)

2. \(a + c > b\):
\(30 + 28 > 60\)
\(58 > 60\) (False)

3. \(b + c > a\):
\(60 + 28 > 30\)
\(88 > 30\) (True)

Since the second condition (\(a + c > b\)) is false, the segments 30, 60, and 28 cannot form a triangle.