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)
Responses
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 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 greater than the third side.
No, because the sum of any two sides is greater 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 less than the third side.
No, because the sum of any two sides is less than the third side.
To determine whether the sides with lengths of 4.24 inches, 9.89 inches, and 8.75 inches form a triangle, we can apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Let's check if this condition is satisfied for the given lengths:
1. The sum of 4.24 inches and 9.89 inches is 14.13 inches, which is greater than 8.75 inches. So, the condition is satisfied for these two sides.
2. The sum of 4.24 inches and 8.75 inches is 13.99 inches, which is also greater than 9.89 inches. Again, the condition is satisfied.
3. Finally, the sum of 9.89 inches and 8.75 inches is 18.64 inches, which is greater than 4.24 inches. The condition is satisfied for these two sides as well.
Since the sum of any two sides is greater than the third side in all cases, we can conclude that the given side lengths of 4.24 inches, 9.89 inches, and 8.75 inches do form a triangle. Therefore, the correct response is:
Yes, because the sum of any two sides is greater than the third side.