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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`.
Solution
Steps of construction:
- Draw a line segment BC = 6 cm.
- Taking B and C as centres, draw two arcs of radii 4 cm and 5 cm intersecting each other at A.
- Join BA and CA. ∆ABC is the required triangle.
- From B, draw any ray BX downwards making at acute angle.
- Mark five points B1, B2, B3, B4 and B5 on BX, such that BB1 = B1B2 = B2B3 = B3B4 = B4B5.
- Join B3C and from B5 draw B5M || B3C intersecting the extended line segment BC at M.
- 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.
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