Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point) Responses They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side. They will form a triangle because the sum of any two of the side lengths is less than the length of the third side. They will form a triangle because the sum of any two of the side lengths is less than the length of the third side. They cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.

Answer 1

To determine whether the side lengths 6 cm, 8 cm, and 10 cm will form a triangle, we can use 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.

Let's verify this for the given side lengths:

1. 6 cm + 8 cm > 10 cm:

   • 14 > 10 (True)

2. 6 cm + 10 cm > 8 cm:

   • 16 > 8 (True)

3. 8 cm + 10 cm > 6 cm:

   • 18 > 6 (True)

Since all three conditions are satisfied, we conclude that these side lengths can indeed form a triangle.

The appropriate response is: They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.