Question
Construct a right-angled triangle whose perimeter is equal to $10\ cm$ and one acute angle equal to $60^\circ$.
✓
Answer
Steps of Construction:
$1.$ Draw a line segment $XY$ of $10\ cm$.
$2.$ Draw $\angle\text{DXY}=90^\circ$ and $\angle\text{EYX}=60^\circ.$
$3.$ Draw the angle bisectors of $\angle\text{DXY}$ and $\angle\text{EYX}$ which intersect each other at $A$.
$4.$ Draw the perpendicular bisector of $AX$ and $AY$ which intersect $XY$ at $B$ and $C$ respectively.
$5.$ Join $AB$ and $AC$.
Hence $\triangle\text{ABC}$ is the required triangle.
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