Question

triangle can be formed with sides 8, 10 and 3 true or false

Answer 1

To determine if a triangle can be formed with the sides 8, 10, and 3, we can use the triangle inequality theorem. This theorem states that for any triangle with sides \( a \), \( b \), and \( c \), the following inequalities must hold:

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

Let's apply these inequalities to the sides 8, 10, and 3.

1. \( 8 + 10 > 3 \)
- \( 18 > 3 \) (True)

2. \( 8 + 3 > 10 \)
- \( 11 > 10 \) (True)

3. \( 10 + 3 > 8 \)
- \( 13 > 8 \) (True)

All three inequalities are satisfied, so it is true that a triangle can be formed with sides 8, 10, and 3.