Given:
- In triangle ABC, AB = 10√3, BC = 20, and angle A = 90 degrees.
- An equilateral triangle ABD is constructed with base AB and vertex D at a maximum possible distance from C.

To find:
The length of CD.

Approach:
To find the length of CD, we need to determine the position of point D and the relationship between CD and the dimensions of triangle ABC.

Solution:

Step 1: Construct triangle ABC:
- Draw a line segment AB of length 10√3 units.
- From point B, draw a perpendicular line segment BC of length 20 units, intersecting AB at point C.
- Join points A and C to form triangle ABC, with angle A = 90 degrees.

Step 2: Construct equilateral triangle ABD:
- Extend the line segment AB beyond point B.
- With B as the center, draw an arc with a radius equal to the length of AB, intersecting the extended line segment at point D.
- Join points A and D to form equilateral triangle ABD.

Step 3: Determine the position of point D:
- To find the maximum possible distance of point D from C, we need to place point D on the same line as BC, in the direction away from point C.
- This ensures that CD is at its maximum length.

Step 4: Relationship between CD and dimensions of triangle ABC:
- Since triangle ABD is equilateral, all sides are equal in length.
- Therefore, AD = AB = 10√3 units.
- CD is the vertical distance between BC and AD.
- CD = BC - BD.

Step 5: Calculate the length of CD:
- BC is given as 20 units.
- To find BD, we can use the relationship between the sides of a 30-60-90 triangle.
- In triangle ABD, angle ABD = 30 degrees (as it is an equilateral triangle).
- Therefore, angle BDA = 180 - 90 - 30 = 60 degrees.
- In a 30-60-90 triangle, the ratio of the sides opposite the angles is 1:√3:2.
- BD/AB = √3/2
- BD = AB * (√3/2) = 10√3 * (√3/2) = 15 units.
- CD = BC - BD = 20 - 15 = 5 units.

Answer:
The length of CD is 5 units.