Construct a triangle using the given data: Perimeter of triangle … - Vidyadip

Question

Construct a triangle using the given data: Perimeter of triangle is $10.6 \ cm$, and the base angles are $60^\circ $ and $45^\circ $

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Answer

Perimeter of triangle is $10.6 \ cm$, and the base angles are $60^\circ $ and $45^\circ $

Steps of construction:
$1.$ Draw $DE = 10.6 \ cm.$
$2.$ Draw $DP$ and $EQ$ such that $\angle PDE = 90^\circ $ and $\angle QED = 60^\circ .$
$3$. Draw $AD$ and $AE$, the bisectors of angles $PDE$ and $QED$ 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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