Question

Construct $\Delta LMN$ such that LM = 6.6 cm, $\angle LNM={65}^o$ and ND is median and ND = 5 cm.

Answer 1

1. Draw base $LM$ of length $6.6cm$. Draw the perpendicular bisector of $LM$ and mark the midpoint as $D$.

2. Draw angles of ${90}^{\circ }-{65}^{\circ }={25}^{\circ }$ from $L$ and $M$ and let them intersect the perpendicular bisector at $O$.

3. With $O$ as the centre and radius $OL$, draw a circle which passes through $L$ and $M$.

4. Take the radius of $ND=5cm$ on the compass and mark an arc on the circle taking $D$ as the centre. Mark the point as $N$.

5. Join $L-N$ and $M-N$.

$△LMN$ is the required triangle.