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
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 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 less 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 greater 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 given side lengths of 4.24 inches, 9.89 inches, and 8.75 inches form a triangle, we can apply the Triangle Inequality Theorem. According to the theorem, for a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check this condition for the given lengths:
1. Sum of 4.24 inches and 9.89 inches: 4.24 + 9.89 = 14.13 inches
Is 14.13 inches greater than 8.75 inches? Yes.
2. Sum of 4.24 inches and 8.75 inches: 4.24 + 8.75 = 12.99 inches
Is 12.99 inches greater than 9.89 inches? Yes.
3. Sum of 9.89 inches and 8.75 inches: 9.89 + 8.75 = 18.64 inches
Is 18.64 inches greater than 4.24 inches? Yes.
Since the sum of the lengths of any two sides is greater than the length of the third side in all three cases, we can conclude that the sides with 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.