Triangle Inequality Theorem Quick Check

Question

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Question
Apply the Triangle Inequality Theorem to determine whether a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters.(1 point)
Responses

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

No, because the sum of any two sides is less than the third side.
No, because the sum of any two sides is less than the third side.

No, because the sum of any two sides is greater than the third side.
No, because the sum of any two sides is greater than the third side.

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

Answer 1

To determine if a triangle can be formed from sides of lengths 7 mm, 8 mm, and 9 mm, we need to apply the Triangle Inequality Theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the conditions:

1. \(7 + 8 = 15 > 9\) (True)
2. \(7 + 9 = 16 > 8\) (True)
3. \(8 + 9 = 17 > 7\) (True)

Since all three conditions are satisfied, we conclude that a triangle can indeed be formed from these side lengths.

The correct response is: Yes, because the sum of any two sides is greater than the third side.