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Seg AD and seg BE are medians of ???? ABC and point G is the centroid. If l(AG) = 5 cm, find l(GD). If l(GE) = 2 cm, find l(BE).

Answer»

Did you know about one THING ?
\bf{Centroid} divides MEDIAN in 2 :1 ratio.

in simple way, if ∆ABC is a TRIANGLE where AD and BE are medians . both AD and BE intersect at a POINT G , it is not other than Centroid.
now, from above concept .
G divides AD in 2 : 1 ratio.
e.g., AG/GD = 2/1
Given, AG = 5 cm
then, GD = AG/2 = 5cm/2 = 2.5 cm
hence, length of GD = 2.5 cm

similarly, G divides BE in 2 : 1 ratio
e.g., BG/GE = 2/1
given, GE = 2 cm
then, BG = 2 × GE = 2 × 2 = 4cm
now, length of BE = BG + GE = 4cm + 2cm
length of BE = 6cm


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