Question

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?

Answer 1

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