Given:
The sides of a triangles in the options.
To find:
Which of the following cannot be the lengths of the sides of a triangle?
Solution:
In a triangle, the sum of two smaller sides must be greater than the longest side, otherwise it cannot be the lengths of the sides of a triangle.
For option A,
[tex]6+8=14>12[/tex]
For option B,
[tex]4+4=8>12[/tex]
For option C,
[tex]6+6=12[/tex]
Here the sum of two smaller sides is not greater than the longest side. So, the sides 6, 6, 12 cannot be the lengths of the sides of a triangle.
For option D,
[tex]6+8=14>10[/tex]
Therefore, the correct option is C.
