Construct a triangle with sides 5cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.

The steps involved in the required construction are:

1) Draw a line segment BC=6 cm.

2) Taking B as the center and radius 5 cm, draw an arc. Now taking C as the center and radius 7 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 5 more times to get points G, H, I, J and K. Join CI.

4) Taking I as the center and any radius, draw an arc., intersecting BD and CI at L and M respectively. Taking K as the center and radius IL, draw an arc., intersecting BD at N. Taking N as the center and radius LM, draw an arc, intersecting previous arc at O. Join and extend KO, intersecting extended BC at P.

5) Taking C as the center and any radius, draw an arc., intersecting BC and CA at R and S respectively. Taking P as the center and radius CR, draw an arc., intersecting BP at T. Taking T as the center and radius RS, draw an arc, intersecting previous arc at U. Join and extend PU, intersecting extended AB at Q.

6) ∆BPQ is the required triangle.