92.

Construct a triangle similar to given ABC in which AB = 4 cm, BC = 6 cm and ∠ABC = 60°, such that each side of the new triangle is 3/4 of given Δ ABC.

Steps of Construction :

1.    Draw a line segment BC = 6 cm.
2.    At B make ∠CBY = 60°.
3.    Take B as centre and radius = AB = 4 cm, draw an arc cutting BY at A.
4.    Join CA to obtain the triangle ABC.
5.    Draw any ray BX making an acute angle with BC on the opposite side of the vertex A.
6.    Mark off 4 (the greater of 3 and 4 in 3/ 4) points B₁, B₂, B₃ and B₄ on BX so that
BB₁ = B₁B₂ = B₂B₃ = B₃B₄

7.    Join B₄C and draw a line through B₃ (the third point, 3 being smaller of 3 and 4 in 3/4), parallel to B₄C to intersect BC at C’.
8.    Draw a line through C’ parallel to the line CA to intersect BA at A’ (see Fig.) Thus, ΔA ‘BC’ is the required triangle.