Question

Construct a triangle whose perimeter is $9.8cm$ and the base angles are ${45}^{\circ }$ and ${60}^{\circ }$.

Answer 1

1. Draw a line $PQ$ such that $PQ=AB+BC+AC=9.8cm.$

2. Construct angle $P={60}^{\circ }$ and angle $Q={45}^{\circ }$.

3. Bisect both angles. Let the angle bisectors meet at $A.$

4. Join $A-P$ and $A-Q.$

5. Draw perpendicular bisectors of $AP$ and $AQ.$

6. Perpendicular bisector of $AP$ meet $PQ$ at $B$ and that of $AQ$ at $C$.

7. Join $A-B$ and $A-C$.

8. $ABC$ is the required triangle.