Construct a ΔABC in which BC = 5 cm, ∠C = 60° and altitude from A equal to 3 cm. Construct a ΔADE similar to ΔABC such that each side of Δ ADE is times the corresponding side of ΔABC. Write the steps of construction.

Steps of Construction:

1. Draw a line segment BC = 5 cm.

2. Draw ∠ ECB = 60°.

3. Draw a line parallel to BC at a distance of 3 cm. Let it intersect EC at A.

4. Join AB.

5. Δ ABC is the required triangle.

6. Draw a ray BX on the side opposite to the vertex A. Also, ∠ CBX should be acute.

7. Along BX, mark 3 points C₁, C₂, C₃ such that BC₁ = C₁C₂ = C₂C₃.

8. Join C₂C.

9. Draw C₃C’ parallel to C₂C such that C’ lies on the extended line BC.

10. Draw C’A’ parallel to AC such that A’ lies on extended BA.

Δ A’BC’ is the required triangle whose sides are times the sides of Δ ABC.