Question

Triangle inequality theorem quick check
Apply the triangle inequality theorem to determine whether sides with lengths of 4 inches, 8 inches and 9 inches form a triangle
Yes, the majority of the conditions are met
No, because two out of three conditions are met
No, all of the conditions are not met
Yes, all of the conditions are met

Answer 1

To determine if the sides with lengths of 4 inches, 8 inches, and 9 inches can form a triangle, we apply the triangle inequality theorem, which states that for any triangle with sides \( a \), \( b \), and \( c \), the following conditions must be met:

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

Let's check these conditions for the given sides:

- Let \( a = 4 \), \( b = 8 \), and \( c = 9 \).

1. \( 4 + 8 > 9 \) → \( 12 > 9 \) (True)
2. \( 4 + 9 > 8 \) → \( 13 > 8 \) (True)
3. \( 8 + 9 > 4 \) → \( 17 > 4 \) (True)

Since all three conditions are met, the answer is:

**Yes, all of the conditions are met.**