To determine if a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this holds true for the given side lengths:
1. The sum of the lengths of the sides 7 millimeters and 8 millimeters is 7 + 8 = 15 millimeters.
- 15 millimeters is greater than 9 millimeters (the length of the remaining side).
2. The sum of the lengths of the sides 7 millimeters and 9 millimeters is 7 + 9 = 16 millimeters.
- 16 millimeters is greater than 8 millimeters (the length of the remaining side).
3. The sum of the lengths of the sides 8 millimeters and 9 millimeters is 8 + 9 = 17 millimeters.
- 17 millimeters is greater than 7 millimeters (the length of the remaining side).
Since the sum of the lengths of any two sides is always greater than the length of the third side in all cases, a triangle can be formed with side lengths of 7 millimeters, 8 millimeters, and 9 millimeters.
Apply the Triangle Inequality Theorem to determine whether a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters
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