Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 cm, 7 cm, and 8 cm form a triangle.(1 point)

Question

Responses

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 two out of three conditions are met.
No, because two out of three conditions are met.

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.

Answer 1

To determine if the sides with lengths 3 cm, 7 cm, and 8 cm can form a triangle, we can apply the Triangle Inequality Theorem. The 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.

Let's check the three conditions:

1. \(3 + 7 > 8\) → \(10 > 8\) (True)
2. \(3 + 8 > 7\) → \(11 > 7\) (True)
3. \(7 + 8 > 3\) → \(15 > 3\) (True)

Since all three conditions are met, the sides do satisfy the Triangle Inequality Theorem.

Therefore, the correct response is:

Yes, because the sum of any two sides is greater than the third side.