Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4.24 inches, 9.89 inches, and 8.75 inches form a triangle. (1 point)
O No, because the sum of any two sides is less than the third side.
O Yes, because the sum of any two sides is greater than the third side.
O No, because the sum of any two sides is greater than the third side.
O Yes, because the sum of any two sides is less than the third side.
O Yes, because the sum of any two sides is greater than the third side.
To apply the Triangle Inequality Theorem, you need to determine whether the sum of any two sides is greater than the third side.
Let's check:
1) Add the lengths of the first two sides: 4.24 + 9.89 = 14.13 inches.
Is 14.13 greater than 8.75? Yes.
2) Add the lengths of the second and third sides: 9.89 + 8.75 = 18.64 inches.
Is 18.64 greater than 4.24? Yes.
3) Add the lengths of the first and third sides: 4.24 + 8.75 = 13.99 inches.
Is 13.99 greater than 9.89? Yes.
According to the Triangle Inequality Theorem, for any triangle, the sum of any two sides must be greater than the third side. Since this condition is satisfied for the given sides (4.24, 9.89, and 8.75 inches), we can conclude that they do form a triangle-
Therefore, the correct answer is:
O Yes, because the sum of any two sides is greater than the third side.
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's check if the given sides of lengths 4.24 inches, 9.89 inches, and 8.75 inches satisfy this theorem.
Adding the first two sides, we have 4.24 + 9.89 = 14.13 inches.
Since 14.13 is greater than the third side, 8.75 inches, this means that the sum of any two sides is indeed greater than the third side.
Therefore, the correct answer is:
O Yes, because the sum of any two sides is greater than the third side.