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To determine which sets of lengths can form a triangle, you should apply the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's evaluate each option:

1. 9 см, 18 см, 15 см

   • 9 + 18 > 15
   • 9 + 15 > 18
   • 18 + 15 > 9
   • All conditions are satisfied.

2. 21.5 см, 6 см, 15 см

   • 21.5 + 6 > 15
   • 21.5 + 15 > 6
   • 6 + 15 = 21, which is not greater than 21.5

3. 18.5 см, 25.5 см, 39.5 см

   • 18.5 + 25.5 = 44, which is greater than 39.5
   • 18.5 + 39.5 > 25.5
   • 25.5 + 39.5 > 18.5
   • All conditions are satisfied.

4. 29.5 см, 5 см, 45 см

   • 29.5 + 5 = 34.5, which is not greater than 45

5. 15 см, 15 см, 15 см

   • 15 + 15 > 15
   • This is an equilateral triangle, and therefore valid.

6. 6 см, 5 см, 15 см

   • 6 + 5 = 11, which is not greater than 15

7. 16 см, 10 см, 32 см

   • 16 + 10 = 26, which is not greater than 32

The valid sets of lengths that can form a triangle are:

• 9 см, 18 см, 15 см
• 18.5 см, 25.5 см, 39.5 см
• 15 см, 15 см, 15 см