Draw a Δ ABC with sides BC = 5cm, AB = 6cm and AC = 7cm and then construct a triangle similar to ΔABC whose sides are 4/7 of the corresponding sides of ΔABC.(CBSE 2016)

Steps of construction :

1. Draw a line AB = 6 cm

2. Taking A as center and with radius = 7 cm, draw an arc.

3. Taking B as center and with radius = 5 cm draw an arc which intersects previous arc at C

4. Join AC and BC to get ∆ABC

5. Below AB, make an acute angle ∠BAX

6. Along AX mark 7 (greater of 4 and 7 in 4/7) points A1, A2, A3, A4, A5, A6 and A7 at equal distances.

7. Join A7B

8. From point A4, make a line A4B' parallel to A7B, meeting AB at B'.[Choosing A4 because we need a 4 : 7 ratio]

9. From point B' draw a line B'C' parallel to BC.

10. AB'C' is the triangle, whose sides are four - seventh of ∆ABC