To construct a triangle ABC with AB = 5cm, BC = 6cm angle ABC = 60 degree, we follow the given steps

1. Draw a line BC = 6 cm

2. Now, take any radius (less than half of BC) and take B as the center, draw an arc that intersects at line BC at

P. With the same radius and center as P, draw another arc that intersects the previous arc at Q.

3. Join BQ and extend it to D

4. Now, take radius 5 cm and center B, draw an arc that intersects line BD at A  

5. Join AC and get the triangle ABC.

6. Draw a line BX as angle CBX is an acute angle and draw seven equal radius arcs on the line BX that

intersects at x₁ , x₂ , x₃ , x₄ , x₅ , x₆ , x₇ as:

 Bx₁ = x₁ x₂ = x₂ x₃ =x₃ x₄ =x₄ x₅ =x₅ x₆ =x₆ x₇ =

7. Join x₇ to C and then draw a line x₅ as parallel to x₇ C that intersects the line BC at C₁

8. Draw line from C₁ as parallel to AC that intersects line AB at A₁

So, we get the triangle A₁ BC₁ whose sides are 5/7 of corresponding sides of triangle ABC.