Question

Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 cm, 7 cm, and 8 cm 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 two out of three conditions are met.

Answer 1

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

We need to check the following conditions:

1. \( 3 + 7 > 8 \)
2. \( 3 + 8 > 7 \)
3. \( 7 + 8 > 3 \)

Let's evaluate each condition:

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

Since all three conditions are met, the sides 3 cm, 7 cm, and 8 cm can indeed form a triangle.

The correct response is: **Yes, because the sum of any two sides is greater than the third side.**