Question

Construct a triangle such that the lengths of its three medians are $4.2$ m, $4.8$cm and $5.4$ cm respectively.

Answer 1

Steps of construction :
1. 1. Draw $AG=2.8$ cm and produce to a point $P$ such that $AG=GP$.
2. From centre $G$, cut an arc
$GC=\frac{2}{3}\times CF=\frac{2}{3}\times 5.4=3.6$ cm
and from $P$ cut an arc
$CP=BG=\frac{2}{3}\times BE$
$=\frac{2}{3}\times 4.8=3.2$ cm
to intersect each other at $C$.
3. From centre $G$, cut an arc
$GB=\frac{2}{3}\times BE=3.2$ cm and from $P$ cut an arc $PB=CG=3.6$ cm to intersect each other at $B$. Draw $BC$.
4. Join $A$ to $B$ and $A$ to $C$.
Hence, $\Delta ABC$ is the required triangle.