Question

Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle.(1 point)
Responses

No, because two out of three conditions are met.
No, because two out of three conditions are met.

No, all of the conditions are not met.
No, all of the conditions are not met.

Yes, the majority of the conditions are met.
Yes, the majority of the conditions are met.

Yes, all of the conditions are met.

Answer 1

To determine whether the sides of lengths 4 inches, 8 inches, and 9 inches can form a triangle, we can apply the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following inequalities must hold:

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

Let's denote the sides as \( a = 4 \), \( b = 8 \), and \( c = 9 \). Now we will check each condition:

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 sides do form a triangle.

So the correct response is:
**Yes, all of the conditions are met.**