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

Answer 1

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

Let’s check the three conditions:

1. \(7 + 8 > 9 \)
   \(15 > 9\) (True)

2. \(7 + 9 > 8\)
   \(16 > 8\) (True)

3. \(8 + 9 > 7\)
   \(17 > 7\) (True)

Since all three conditions are satisfied, the correct answer is:

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