Question

Construct a $\Delta$ PQR in which the base PQ$=6$cm, $\angle$R$={60}^o$ and the altitude from R to PQ is $4$cm.

Answer 1

$Step1:$ Draw a line segment $PQ=6cm$

$Step2:$ At $P$, make $\angle QPX={60}^0$.

$Step3:$ Draw $PY\perp PX$.

$Step4:$Draw the perpendicular bisector of $PQ$ which meets $PY$ at $O$.

$Step5:$ With $O$ as center and $OP$ as radius draw a circle.

$Step6:$ On the perpendicular bisector $MO$, mark a point $S$ such that $MS=4cm$.

$Step7:$ Draw $RS{R}^{\prime }$ parallel to $PQ$ meeting the circle at $R$ and at $R^{\prime }.$

$Step8:$ Complete $△PQR$ which is one of the required triangles.