Question Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point) Responses 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 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 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 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 greater than the length of the third side.

Answer 1

To determine whether the side lengths of 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 of 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 three conditions:

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 of the triangle inequality are satisfied, the side lengths 6 cm, 8 cm, and 10 cm can indeed 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.