Triangle Inequality Theorem Quick Check

Question

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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.
Yes, all of the conditions are met.

Answer 1

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

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

Let's check these conditions with the given side lengths:

• Let \( a = 4 \), \( b = 8 \), 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 answer is:

Yes, all of the conditions are met.