Construct a right triangle whose base is $6\,cm$ and the sum of its hypotenuse and the other side is $12\,cm$. Write the steps of construction.
(N/A) $1$. Draw a line segment $AB = 6\,cm$ as the base.
$2$. At point $B$,construct an angle of $90^\circ$ using a compass.
$3$. From the ray $BX$ (making $90^\circ$ with $AB$),cut off a line segment $BD = 12\,cm$.
$4$. Join $AD$.
$5$. Draw the perpendicular bisector of $AD$,which intersects $BD$ at point $C$.
$6$. Join $AC$. Thus,$\triangle ABC$ is the required right-angled triangle where $BC + AC = 12\,cm$ and $AB = 6\,cm$.
$2$. At point $B$,construct an angle of $90^\circ$ using a compass.
$3$. From the ray $BX$ (making $90^\circ$ with $AB$),cut off a line segment $BD = 12\,cm$.
$4$. Join $AD$.
$5$. Draw the perpendicular bisector of $AD$,which intersects $BD$ at point $C$.
$6$. Join $AC$. Thus,$\triangle ABC$ is the required right-angled triangle where $BC + AC = 12\,cm$ and $AB = 6\,cm$.
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