To determine if three side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three sides \( a \), \( b \), and \( c \) (where the sides are ordered such that \( a \leq b \leq c \)), the following must hold:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
For the side lengths given: 6 cm, 8 cm, and 10 cm:
- \( 6 + 8 = 14 \) which is greater than \( 10 \)
- \( 6 + 10 = 16 \) which is greater than \( 8 \)
- \( 8 + 10 = 18 \) which is greater than \( 6 \)
Since all three conditions are satisfied, the 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.