In a triangle ABC if the equation of the medians AD and BE are #2x+3y-6=0# and #3x-2y-10=0# respectively and AD = 6 and BE = 11, then find the area of the triangle ABC?

1 Answer
P dilip_k
Mar 15, 2018

drawn
Let the point of intersection of medians #AD and BE# be G.

The Slope of #AD # obtained from its given equation #2x+3y-6=0# is #m_1=-2/3# and the Slope of #BE # obtained from its given equation #3x-2y-10=0# is #m_2=3/2#.

As #m_1xxm_2=-2/3xx3/2=-1# then angle between the medians #AD# and #BE# at #G# is #angleAGB=90^@#

Now #AG=2/3xxAD=2/3xx6=4#

And #BG=2/3xxBE=2/3xx11=22/3#

So area of the #DeltaABG==1/2xxAGxxBG#

#=>DeltaABG=1/2xx4xx22/3=44/3# squnit

Now Area of #Delta ABC=3xxDelta ABG=3xx44/3=44# squnit

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