Online Course Discussion Forum

Winter Camp 2018 Blue Geometry question 3

 
 
wangXin的头像
Winter Camp 2018 Blue Geometry question 3
wangXin 发表于 2019年01月20日 Sunday 16:34
 

Let G be the centroid of triangle ABC, AG is 3, BG is 4, CG is 5, find the area of ABC

 
ReynosoDavid的头像
Re: Winter Camp 2018 Blue Geometry question 3
ReynosoDavid 发表于 2019年01月22日 Tuesday 17:55
 

Extend line $AG$ to a point $H$, so that $GH = 3$. Then $GBHC$ is a parallelogram with sides $4$ and $5$, and one of its diagonals of length $3$ (why?).  What else can you say about this parallelogram? Can you find its area? How does the area of this parallelogram relate to the area of the triangle?

* Recall that the centroid splits each median in a $2:1$ ratio, and the $6$ triangles made up by the medians all have the same area.

wangXin的头像
Re: Winter Camp 2018 Blue Geometry question 3
wangXin 发表于 2019年01月22日 Tuesday 18:16
 

Did not get this one yet.