Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 inches, 4 inches, and 9 inches form a triangle. (1 point)
O Yes, the majority of the conditions are met.
O Yes, because 3 + 4 is less than 9.
O No, because 3 + 4 is less than 9.
O Yes, because the sum of any two sides is less than the third side.
O No, because 3 + 4 is less than 9.
The correct answer is:
O No, because 3 + 4 is less than 9.
To apply the Triangle Inequality Theorem, we need to check if the sum of any two sides of a triangle is greater than the third side.
In this case, we have sides with lengths of 3 inches, 4 inches, and 9 inches. Let's check if the sum of any two sides is greater than the third side:
1. 3 + 4 = 7, which is less than 9.
2. 3 + 9 = 12, which is greater than 4.
3. 4 + 9 = 13, which is greater than 3.
Since the sum of any two sides is greater than the third side (conditions 2 and 3), we can conclude that this set of side lengths does form a triangle. Therefore, the correct option would be:
O Yes, because the sum of any two sides is less than the third side.