Question

Construct a triangle $ABC$, in which $BC=6.5cm,\angle A={60}^o$ and median$=4.5$cm

Answer 1

Given: In $△ABC,BC=6.5cm,\angle A={60}^o$ and median $AD=4.5cm$
To construct: $△ABC$

Steps for construction:
(i) Draw line segment $BC=6.5cm$
(ii) At point $B$ draw $\angle CBK={60}^o$, below $BC$.
(iii) Draw $BL\perp BK$
(iv) Draw perpendicular bisector $PQ$ of $BC$, which intersects $BC$ at point $D$.
(v) Taking the point of intersection of $BL$ and $PQ$ as centre and $OB$ as radius, draw a circle.
(vi) Taking point $D$ at $PQ$ as centre draw an arc of $AD=4.5cm$ at circumference of the circle and let $A$ and $A^{\prime }$ be points of intersection.
(vii) Join $AB,AC,A^{\prime }B,A^{\prime }c$
The $△ABC$ and $△A^{\prime }BC$ thus obtained are the required triangle.