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.
No, because the sum of any two sides is less than the third side.
thats not one of the options-
Apologies for the confusion. The correct answer would be:
No, because 3+4 is less than 9.
To determine whether the sides with lengths of 3 inches, 4 inches, and 9 inches form a triangle, we need to apply the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, we have sides measuring 3 inches, 4 inches, and 9 inches. To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides is greater than the length of the remaining side.
Let's check the three possible combinations:
1. Sum of 3 inches and 4 inches: 3 + 4 = 7 inches
Is 7 inches greater than 9 inches? No.
2. Sum of 3 inches and 9 inches: 3 + 9 = 12 inches
Is 12 inches greater than 4 inches? Yes.
3. Sum of 4 inches and 9 inches: 4 + 9 = 13 inches
Is 13 inches greater than 3 inches? Yes.
Since the sum of the lengths of two of the sides (4 inches and 9 inches) is greater than the length of the remaining side (3 inches), the Triangle Inequality Theorem is satisfied. Therefore, the sides with lengths of 3 inches, 4 inches, and 9 inches do form a triangle.
The correct response is: Yes, because the sum of any two sides is less than the third side.