Let AC be x cm
then AE = x/4 cm

since. BC II DE
therefore. AD/AB = AE/AC. (BPT)
or. AD/6 = (x/4)/x ( AB =6 CM )
or. AD/6 = x/4x
or. AD/6 = 1/4
OR. AD. = 6/4
OR. AD = 1.5 CM

Given:
- In triangle ABC, AB = 6 cm.
- DE is parallel to BC.
- AE = 1/4 AC.

To find:
- Length of AD.

Solution:
Step 1: Understanding the problem
We are given a triangle ABC, where AB = 6 cm. We need to find the length of AD. To solve this problem, we can use the concept of similar triangles.

Step 2: Drawing a diagram
Let's draw a diagram to visualize the given information.
[Insert a diagram of triangle ABC with points A, B, C, D, E labeled.]

Step 3: Identifying similar triangles
From the given information, we can observe that triangle ADE is similar to triangle ABC. This is because DE is parallel to BC, and AE/AC = 1/4.

Step 4: Using the concept of similar triangles
Since triangle ADE is similar to triangle ABC, the corresponding sides of these triangles are proportional. Let's denote the length of AD as x.

By the property of similar triangles, we have:

AD/AB = AE/AC

Substituting the given values, we get:

x/6 = 1/4

Step 5: Solving for x
To find the value of x, we can cross multiply the equation:

4x = 6

Dividing both sides by 4, we get:

x = 6/4

Simplifying the fraction, we have:

x = 3/2

Therefore, the length of AD is 3/2 cm or 1.5 cm.

Step 6: Final answer
After solving the equation, we found that the length of AD is 1.5 cm.