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. 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. No, because the sum of any two sides is greater 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 with sides of lengths \(a\), \(b\), and \(c\):

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

Let's check each of the conditions using the given lengths:

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, it is concluded that a triangle can indeed be formed from sides of lengths 7 mm, 8 mm, and 9 mm.

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