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Question
Construct an equilateral triangle of side 7 cm. Now, construct another triangle similar to the first triangle such that each of its sides are `5/7` times of the corresponding sides of the first triangle.
Solution
Steps of construction:
- Draw a line segment LM = 7 cm.
- Draw an arc with M as centre and radius = 7 cm.
- Draw another arc with L as the centre and radius = 7 cm that cuts the previous arc at N.
- Join LN and MN. Thus, ΔLMN is obtained.
- Draw an acute ∠MLX below LM.
- Mark seven points L1, L2, L3, ...... , L7 along LX such that, LL1 = L1L2 = L1L3 = ...... = L6L7.
- Join L7M.
- Draw L5M' || L7M that meets LM at M'.
- Draw M'N' || MN that meets LN at N'.
Hence, ΔLM'N' is the required triangle similar to ΔLMN, such that each side of ΔLM'N' is `5/7` of the corresponding side of ΔLMN.
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