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

Answer 1

To determine if the lengths 4 inches, 8 inches, and 9 inches can form a triangle, we apply the Triangle Inequality Theorem. The theorem states that for any three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. We will check the three conditions:

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 lengths of 4 inches, 8 inches, and 9 inches can indeed form a triangle.

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