Steps of Construction:

Step I: A triangle ABC with sides 5 cm, 6 cm and 7 cm is drawn.

Step II: A ray BX making an acute angle with BC is drawn opposite to vertex A.

Step III: 7 points as B1 B2 B3 B4 B5 B6 and B7 are marked on BX.

Step IV; Point B5 is joined with C to draw B5C.

Step V: B7C' is drawn parallel to B5C and C'A' is parallel to CA.

Thus A'BC' is the required triangle.

Justification

ΔAB'C' ~ ΔABC by AAA similarity condition

∴ AB/A'B = AC/A'C' = BC/BC'

And BC/BC' = BB5/BB7 = 5/7

∴A'B/AB = A'C'/AC = = BC'/BC = 7/5