Question
Construct a triangle using the given data: Perimeter of triangle is $6.4 \ cm$, and the base angles are $60^\circ $ and $45^\circ $
✓
Answer
Perimeter of triangle is $6.4 \ cm$, and the base angles are $60^\circ $ and $45^\circ $
Steps of construction:
$1$. Draw $DE = 6.4 \ cm.$
$2$. Draw $DP$ and $EQ$ such that $\angle PDE = 45^\circ $ and $\angle QED = 60^\circ $
$3$. Draw $AD$ and $AE$, the bisectors of angles $\text{PDE}$ and $\text{QED}$ respectively, intersecting each other at $A.$
$4.$ Draw perpendicular bisectors of $AD$ and $AE$, intersecting $DE$ at points $B$ and $C$ respectively.
$5.$ Join $AB$ and $AC.$
Thus, $\text{ABC}$ is the required triangle.
Steps of construction:
$1$. Draw $DE = 6.4 \ cm.$
$2$. Draw $DP$ and $EQ$ such that $\angle PDE = 45^\circ $ and $\angle QED = 60^\circ $
$3$. Draw $AD$ and $AE$, the bisectors of angles $\text{PDE}$ and $\text{QED}$ respectively, intersecting each other at $A.$
$4.$ Draw perpendicular bisectors of $AD$ and $AE$, intersecting $DE$ at points $B$ and $C$ respectively.
$5.$ Join $AB$ and $AC.$
Thus, $\text{ABC}$ is the required triangle.
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