Question

Draw a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Construct a triangle similar to it and of scale factor `5/3`.

Answer 1

Steps of construction:

1. Draw a line segment BC = 6 cm.
2. Taking B and C as centres, draw two arcs of radii 4 cm and 5 cm intersecting each other at A.
3. Join BA and CA. ∆ABC is the required triangle.
4. From B, draw any ray BX downwards making at acute angle.
5. Mark five points B₁, B₂, B₃, B₄ and B₅ on BX, such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅.
6. Join B₃C and from B₅ draw B₅M || B₃C intersecting the extended line segment BC at M.
7. From point M draw MN || CA intersecting the extended line segment BA at N.
   Then, ∆NBM is the required triangle whose sides is equal to `5/3` of the corresponding sides of the ∆ABC.
   Hence, ∆NBM is the required triangle.