Triangle ABC:

To draw triangle ABC, we need to follow the given information:
- Side AB = 3.8cm
- Angle B = 60°
- Median = 3.6cm

Construction Steps:

1. Draw a line segment AB of length 3.8cm.
2. At point A, draw a ray AX making an angle of 60° with AB.
3. Using a compass, open it to a length of 1.8cm (half of the given median length) and draw an arc from point X intersecting the ray AX at point Y.
4. Join points B and Y. This line segment BY will be the median of triangle ABC.

Triangle AB'C:

To draw triangle AB'C, we need to follow the given information:
- Side AB' = (4/3)AB

Construction Steps:

1. Draw a line segment AB of length 3.8cm.
2. Multiply the length of AB by (4/3) to obtain AB'.
AB' = (4/3) * 3.8cm = 5.07cm
3. At point A, draw a ray AX making an angle of 60° with AB.
4. Using a compass, open it to a length of 5.07cm and draw an arc from point X intersecting the ray AX at point Y.
5. Join points B and Y. This line segment BY will be the median of triangle AB'C.

Explanation:

- Triangle ABC is drawn using the given side length AB = 3.8cm and angle B = 60°. The median BY is constructed by drawing an arc from the midpoint of AB to the opposite vertex.
- Triangle AB'C is similar to triangle ABC because both triangles have the same angle measures. To draw AB'C, we multiply the length of AB by (4/3) to obtain the length of AB'. Using this length, we construct triangle AB'C by following the same steps as triangle ABC.
- The triangles ABC and AB'C are similar because they have the same angle measures. This means that corresponding sides of the triangles are in proportion. In this case, AB' is (4/3) times the length of AB, which satisfies the conditions for similarity.

Note:
- The given measurements and construction steps are approximate and can be adjusted according to the available tools and precision required.