Which of the following cannot be the measures of three sides of a triangle?

Correct option is C

To determine which set of sides cannot form a triangle, we use the triangle inequality theorem, which 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.

Checking each option:

1. 5 cm, 10 cm, 6 cm:

   • 5 + 10 = 15, which is greater than 6
   • 10 + 6 = 16, which is greater than 5
   • 5 + 6 = 11, which is greater than 10
     This set can form a triangle.

2. 14 cm, 7 cm, 8 cm:

   • 14 + 7 = 21, which is greater than 8
   • 7 + 8 = 15, which is greater than 14
   • 14 + 8 = 22, which is greater than 7
     This set can form a triangle.

3. 10 cm, 20 cm, 8 cm:

   • 10 + 20 = 30, which is greater than 8
   • 20 + 8 = 28, which is greater than 10
   • 10 + 8 = 18, which is not greater than 20
     This set cannot form a triangle.

4. 30 cm, 20 cm, 12 cm:

   • 30 + 20 = 50, which is greater than 12
   • 20 + 12 = 32, which is greater than 30
   • 30 + 12 = 42, which is greater than 20
     This set can form a triangle.

The set of sides 10 cm, 20 cm, and 8 cm violates the triangle inequality theorem, as the sum of 10 and 8 is less than 20. Therefore, this set cannot form a triangle.