Steps of Construction:

Step I: BC = 6 cm is drawn.

Step II: At point B, AB = 5 cm is drawn making an

∠ABC = 60° with BC.

Step III: AC is joined to form ΔABC.

Step IV: A ray BX is drawn making an acute angle with BC opposite to vertex A.

Step V: 4 points B1 B2 B3 and B4 at equal distance is marked on BX.

Step VII: B3 is joined with C' to form B3C'.

Step VIII: C'A' is drawn parallel CA.

Thus, A'BC' is the required triangle.

Justification:

∠A = 60° (Common)

∠C = ∠C'

ΔAB'C' ~ ΔABC by AA similarity condition.

∴ AB/AB' = BC/B'C' = AC/AC'

Also,

AB/AB' = AA3/AA4 = 4/3

⇒ AB' = 3/4 AB, B'C' = 3/4 BC and AC' = 3/4 AC