Question

7. Draw a line segment AB and by ruler and compasses1 obtain a line segment of length `3/4`AB. 

Answer 1

Steps of construction:
1. Draw a line segment AB
2. With center A and radius more than `1/2` AB, draw arcs one on each side of AB.
3. With center B and same radius draw arcs cutting previous arcs at P and Q respectively.
4. Join PQ and which intersect AB at C
5. With center C and radius more than `1/2`CB draw arcs, one on each side of CB.
6. With center B and same radius, draw arcs cutting previous arcs at R and S respectively.
7. Join RS and which intersect CB at D
  ∴ AD = `3/4`  AB