Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.

The steps involved in the required construction are:

1) Draw a line segment BC= 6 cm.

2) Using a protractor, draw ∠CBD=90°. Taking B as the center and radius 8 cm draw an arc, intersecting BD at A. Join AC.

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

4)Taking I as the center and any radius, draw an arc., intersecting BD and CI at J and K respectively. Taking H as the center and radius IJ, draw an arc., intersecting BD at L. Taking L as the center and radius JK, draw an arc, intersecting previous arc at M. Join and extend HM, intersecting BC at N.

5) Taking C as the center and any radius, draw an arc., intersecting BC and CA at P and Q respectively. Taking N as the center and radius CP, draw an arc., intersecting BC at R. Taking R as the center and radius PQ, draw an arc, intersecting previous arc at S. Join and extend NS, intersecting AB at O.

6) ∆BNO is the required triangle.