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. No, because 3+4 is less than 9. No, 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. Skip to navigation page 8 of 8

Answer 1

To determine whether the lengths of 3 inches, 4 inches, and 9 inches can form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

We can check the following combinations:

1. \(3 + 4 > 9\) (This is false, since \(7 > 9\) is not true.)
2. \(3 + 9 > 4\) (This is true, since \(12 > 4\) is true.)
3. \(4 + 9 > 3\) (This is true, since \(13 > 3\) is true.)

However, since one of the conditions fails (the first one), the lengths cannot form a triangle.

Therefore, the correct response is: No, because 3 plus 4 is less than 9.