Question

Can the three segments form a triangle
10
35
30

Answer 1

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

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

Given the segment lengths \( 10 \), \( 35 \), and \( 30 \), let's check these conditions.

1. \( 10 + 35 > 30 \)
- \( 45 > 30 \) (True)

2. \( 10 + 30 > 35 \)
- \( 40 > 35 \) (True)

3. \( 35 + 30 > 10 \)
- \( 65 > 10 \) (True)

Since all three conditions are satisfied, the segments of lengths \( 10 \), \( 35 \), and \( 30 \) can indeed form a triangle.