Explanation:

- The two circles have radii of 28 cm and 18 cm.

- When they touch externally, the distance between their centers is the sum of their radii: 28 cm + 18 cm = 46 cm.

- For two external circles, the length of the common external tangent can be found using the formula:

$$

\text{Length of tangent} = \sqrt{d^2 - (r_1 - r_2)^2}

$$

where \(d\) is the distance between the centers and \(r_1\) and \(r_2\) are the radii.

- Here, the formula becomes:

$$

\sqrt{46^2 - (28 - 18)^2} = \sqrt{2116 - 100} = \sqrt{2016} \approx 44.90 \, \text{cm}

$$

- Looking at the options:

- Option 1: 40.90 cm

- Option 2: 42.00 cm

- Option 3: 44.90 cm

- Option 4: 44.12 cm

- The correct answer based on this calculation is:

44.90 cm