The steps involved in the required construction are:

1) Draw a line segment BC=6 cm.

2) Taking B as the center and radius 4 cm, draw an arc. Now taking C as the center and radius 5 cm draw another arc, intersecting the previous arc at A. Join AB and AC.

3) Draw any line segment BD, making an acute angle with BC and opposite to the vertex A. Taking B as the center and any radius, draw an arc, intersecting BD at E. Taking E as the center and radius BE, draw an arc, intersecting BD at F. Similarly, repeat the process 2 more times to get points G and H. Join CH.

4) Taking H as the center and any radius, draw an arc., intersecting BD and CH at I and J respectively. Taking G as the center and radius HI, draw an arc., intersecting BD at K. Taking K as the center and radius IJ, draw an arc, intersecting previous arc at L. Join and extend HL, intersecting BC at M.

5) Taking C as the center and any radius, draw an arc., intersecting BC and CA at O and P respectively. Taking M as the center and radius CO, draw an arc., intersecting BC at Q. Taking Q as the center and radius OP, draw an arc, intersecting previous arc at R. Join and extend MR, intersecting AB at N.

6) ∆BMN is the required triangle.