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.

Answer 1

Steps of construction:

1. Draw a line segment LM = 7 cm.
2. Draw an arc with M as centre and radius = 7 cm.
3. Draw another arc with L as the centre and radius = 7 cm that cuts the previous arc at N.
4. Join LN and MN. Thus, ΔLMN is obtained.
5. Draw an acute ∠MLX below LM.
6. Mark seven points L₁, L₂, L₃, ...... , L₇ along LX such that, LL₁ = L₁L₂ = L₁L₃ = ...... = L₆L₇.
7. Join L₇M.
8. Draw L₅M' || L₇M that meets LM at M'.
9. 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.