1.

Construct a triange ABC in which AD,BE and CF are the medians with AD =5.4cm, BE=6 cm and CF=8.1cm.

Answer»

Solution :We KNOW that the centroid G divides each MEDIAN in the ratio `2:1` from the corresponding vertex.
(a) `AG=3.6 cm, GD=1.8 cm``{ :' AD =5.4 cm}`
(b) `BG=4 cm, GE=2cm``{ :' BE=6 cm}`
(c ) `CG=5.4 cm, GF=2.7 cm``{ :' CF =8.1 cm}`
Produce `bar(GD)` to the point H such that `GD=DH=1.8` cm.
Now, BGCH is a parallelogram.


(a) Draw a parallelogram BGCH with `BH=CG=5.4cm, HC=BG=4cm` and `GH=3.6cm`.
(b) JOIN BC.
(c) Produce BG to the point E such that `GE=2cm`.
(d ) Produce CG to the pointsuch that `GF=2.7`cm.
(e) ` Join BF and CE and produce them to meet at point A.
ABC is the requiredtriangle.


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