Triangle Inequality Theorem Quick Check 1 of 51 of 5 Items 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. Yes, all of the conditions are met. Yes, all 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. Skip to navigation

Answer 1

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

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

Let's apply these conditions with the given lengths:

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

Now check the conditions:

1. \(4 + 8 > 9\)

   • This simplifies to \(12 > 9\) (True)

2. \(4 + 9 > 8\)

   • This simplifies to \(13 > 8\) (True)

3. \(8 + 9 > 4\)

   • This simplifies to \(17 > 4\) (True)

Since all three conditions are met, we can conclude that:

Yes, all of the conditions are met.