.

To determine which set of lengths can form a triangle, we need to ensure the triangle inequality holds for each set of lengths. This means that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check each option:

1. 14 cm, 5 cm, 18 cm

   • \(14 + 5 = 19 > 18\)
   • \(14 + 18 = 32 > 5\)
   • \(5 + 18 = 23 > 14\)
     All conditions are satisfied.

2. 11 cm, 8 cm, 20 cm

   • \(11 + 8 = 19 \not> 20\)
     This does not satisfy the triangle inequality.

3. 20 cm, 22 cm, 64 cm

   • \(20 + 22 = 42 \not> 64\)
     This does not satisfy the triangle inequality.

4. 3 cm, 4 cm, 8 cm

   • \(3 + 4 = 7 \not> 8\)
     This does not satisfy the triangle inequality.

5. 11.5 cm, 17.5 cm, 23.5 cm

   • \(11.5 + 17.5 = 29 > 23.5\)
   • \(11.5 + 23.5 = 35 > 17.5\)
   • \(17.5 + 23.5 = 41 > 11.5\)
     All conditions are satisfied.

6. 21.5 cm, 53.5 cm, 37 cm

   • \(21.5 + 37 = 58.5 > 53.5\)
   • \(21.5 + 53.5 = 75 > 37\)
   • \(37 + 53.5 = 90.5 > 21.5\)
     All conditions are satisfied.

The sets of lengths that can form a triangle are:

• 14 cm, 5 cm, 18 cm
• 11.5 cm, 17.5 cm, 23.5 cm
• 21.5 cm, 53.5 cm, 37 cm