Question

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 1

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

Answer 2

It is given that ,

In ∆ABC ,

AD and BE are medians .

I( AG ) = 5 cm ,

I( GE ) = 2 cm ,

We know that ,

Concurrent point of medians is called the

Centroid ( G ) of the triangle .

i ) AG : GD = 2 : 1

5 : GD = 2 : 1

GD = ( 5 × 1 )/2

GD = 2.5 cm

ii ) BE : GE = 3 : 1

BE : 2 = 3 : 1

BE = ( 2 × 3 )/1

BE = 6 cm

Therefore ,

I( GD ) = 2.5 cm

I( BE ) = 6 cm

I hope this helps you.

: )