Triangle Inequality Theorem Quick Check

Question

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Question
Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 inches, 4 inches, and 9 inches form a triangle.(1 point)
Responses

Yes, because 3+4 is less than 9.
Yes, because 3 plus 4 is less than 9.

Yes, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is less than the third side.

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

No, because 3+4 is less than 9.

Answer 1

To determine whether the sides with lengths of 3 inches, 4 inches, and 9 inches can form a triangle using the Triangle Inequality Theorem, we need to check the following conditions:

1. The sum of any two sides must be greater than the third side.

Let's check the inequalities:

1. \(3 + 4 > 9\) → \(7 > 9\) (False)
2. \(3 + 9 > 4\) → \(12 > 4\) (True)
3. \(4 + 9 > 3\) → \(13 > 3\) (True)

Since one of the conditions (3 + 4 > 9) is not satisfied, we conclude that the sides do not form a triangle.

The correct response is:

No, because 3+4 is less than 9.