Question

ΔLMN ~ ΔLQP. In ΔLMN, LM = 3.6 cm, ∠L = 50°, LN = 4.2 cm and `("LM")/("LQ") = 4/7`. Construct ΔLQP.

Answer 1

Steps of construction:

1. Construct △LMN such that LM = 3.6 cm, ∠ L = 50° and LN = 4.2 cm. 
2. Draw ray LX making a suitable angle with LM.
3. Take equal parts LL₁, L₁L₂, L₂L₃, L₃L₄, L₄L₅, L₅L₆, L₆L₇ on ray LX.
4. Join L₄ M.
5. Draw L₇ Q parallel to L₄ M and intersecting ray LM in point Q.
6. Draw QP parallel to MN and intersecting ray LN in point P.
7. △LQP is the required triangle.

Rough figure: