Triangle Inequality Theorem Quick Check

Question

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Question
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.

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.

Answer 1

To determine whether the sides with lengths of 4.24 inches, 9.89 inches, and 8.75 inches can form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

We need to check the following conditions:

1. \( 4.24 + 9.89 > 8.75 \)
2. \( 4.24 + 8.75 > 9.89 \)
3. \( 9.89 + 8.75 > 4.24 \)

Now, let's calculate each condition:

1. \( 4.24 + 9.89 = 14.13 > 8.75 \) (True)
2. \( 4.24 + 8.75 = 13.00 > 9.89 \) (False)
3. \( 9.89 + 8.75 = 18.64 > 4.24 \) (True)

Since the second condition is false, the sides do not satisfy the Triangle Inequality Theorem.

Thus, the answer is:

No, because the sum of any two sides is less than the third side.