Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

The steps involved in the required construction are:

1) Draw a line segment BC= 8 cm.

2) Taking B as the center and any radius greater than , draw two arcs on each side of BC. Taking C as the center and same radius, draw 2 more arcs, intersecting previous arcs at D and E. DE, intersecting BC at F. Taking F as the center and radius 4 cm, draw an arc, intersecting FD at A. Join AB and AC.

3) Draw any line segment BG, making an acute angle with BC and opposite to the vertex A. Taking B as the center and any radius, draw an arc, intersecting BG at H. Taking H as the center and radius BH, draw an arc, intersecting BG at I. Taking I as the center and radius BH, draw an arc, intersecting BG at J. Join CI.

4) Taking I as the center and any radius, draw an arc., intersecting BG and CI at K and L respectively. Taking J as the center and radius IK, draw an arc, intersecting BG at M. Taking M as the center and radius KL, draw an arc, intersecting previous arc at N. Join and extend JN, intersecting extended BC at O.

5) Taking C as the center and any radius, draw an arc., intersecting BC and CA at Q and R respectively. Taking O as the center and radius CQ, draw an arc., intersecting BO at S. Taking S as the center and radius QR, draw an arc, intersecting previous arc at T. Join and extend OT, intersecting extended AB at P.

6) ∆BOP is the required triangle.