**Question:**

Draw a line segment AB and by ruler and compasses, obtain a line segment of length (3/4)(AB).

**Solution:**

Steps of construction:

1. Draw a line segment AB.

2. With A as center and radius more than half of AB draw arcs, one on each side of AB.

3. With B as the center and same radius draw arcs cutting the previous arcs at points P and Q respectively.

4. Join P and Q which intersects AB at C.

5. With A as center and radius more than half of AC draw arcs, one on each side of AC.

6. With C as the center and same radius draw arcs cutting the previous arcs at R and S respectively.

7. Join points R and S which intersects AC at D.

Therefore AD = (3/4) (AB)