Question
Construct a $\triangle\text{ABC},$ with $BC = 7cm,$ $\angle\text{B}=60^\circ$ and AB = 6cm. Construct another triangle whose sides are $\frac34\text{times}$ the corresponding sides of $\triangle\text{ABC}.$
✓
Answer
Steps of Construction:
Step 1. Draw a line segment $BC = 7cm.$
Step 2. At $B,$ draw $\angle\text{XBC}=60^\circ.$
Step 3. With $B$ as centre and radius 6cm, draw an arc cutting the ray $BX$ at $A.$
Step 4. Join $AC.$ Thus, $\triangle\text{ABC}$ is the required triangle.
Step 5. Below BC, draw an acute angle $\angle\text{YBC}.$
Step 6. Along BY, mark four points $B_1, B_2, B_3$ and B_4such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4.$
Step 7. Join $CB_4.$
Step 8. From $B_3,$ draw $B_3C' || CB_4$ meeting $BC$ at $C'.$
Step 9. From $C',$ draw $A'C' || AC$ meeting $AB$ in $A'.$
Here, $\triangle\text{ABC}$ is the required triangle whose sides are $\frac34\text{times}$ the corresponding sides of $\triangle\text{ABC}.$
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