Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)

Question

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 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.

They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.

Answer 1

To determine whether the three side lengths 6 cm, 8 cm, and 10 cm can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the inequalities:

1. 6 cm + 8 cm > 10 cm --> 14 cm > 10 cm (True)
2. 6 cm + 10 cm > 8 cm --> 16 cm > 8 cm (True)
3. 8 cm + 10 cm > 6 cm --> 18 cm > 6 cm (True)

Since all of these conditions are satisfied, the side lengths do form a triangle.

The correct 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.