By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3):(1)/(sqrt(3))`.

Explanation

To divide a line segment in the ratio \(\sqrt{3} : \frac{1}{\sqrt{3}}\), we can simplify this ratio to \(3 : 1\). This means we need to construct a line segment that is divided into two parts where one part is three times the length of the other part.

Here are the step-by-step instructions for the construction:

### Step 1: Draw a Line Segment
- Draw a line segment \(AB\) of any convenient length. Let's say the length of \(AB\) is \(4\) cm.

**Hint:** You can use a ruler to draw a straight line segment.

### Step 2: Mark Points
- Mark point \(A\) at one end of the line segment and point \(B\) at the other end.

**Hint:** Label the points clearly to avoid confusion later.

### Step 3: Extend the Line Segment
- Extend the line segment \(AB\) in the direction of \(B\) to a point \(C\) such that \(AC = 3 \times AB\). Since \(AB\) is \(4\) cm, \(AC\) should be \(12\) cm.

**Hint:** Use the ruler to measure the extended length accurately.

### Step 4: Draw a Circle
- With point \(A\) as the center, draw a circle with radius \(AC\) (which is \(12\) cm).

**Hint:** Use a compass to ensure the circle is drawn accurately.

### Step 5: Draw a Perpendicular Line
- From point \(B\), draw a perpendicular line to the line segment \(AC\). This can be done using a set square or by constructing a right angle.

**Hint:** Ensure that the perpendicular line is straight and intersects the circle.

### Step 6: Mark Intersection Point
- Let the perpendicular line intersect the circle at point \(D\).

**Hint:** Label this intersection point clearly.

### Step 7: Measure the Ratio
- Now, measure the lengths \(AD\) and \(DB\). You should find that \(AD\) is three times the length of \(DB\).

**Hint:** Use the ruler to measure the segments accurately.

### Conclusion
You have successfully divided the line segment \(AB\) in the ratio \(\sqrt{3} : \frac{1}{\sqrt{3}}\) or \(3 : 1\).

---