Question

Construct a $\Delta$ ABC in which AB = 4 cm, $\angle$ B = ${60}^{\circ }$ and altitude CL = 3 cm. Construct a $\Delta$ ADE similar to $\Delta$ ABC such that each side of $\Delta$ ADE is $\frac{3}{2}$ times that of the corresponding side of $\Delta$ ABC

Answer 1

Steps of construction:

1. Construct a $\Delta$ ABC with given measurement

2. Extend AB to D such that $AD=\frac{3}{2}AB=(\frac{3}{2}\times 4)cm=6cm$

3. Draw $DE\parallel BC$, cutting AC produced at E.

4. $\Delta$ ADE is the required triangle similar to $\Delta$ ABC such that each side of $\Delta$ ADE is $\frac{3}{2}$ times the corresponding
side of $\Delta$ ABC.