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# The triangle ABC,right-angled at C,has median AD.BE and CF. AD lies along the line y=x+3,BE lies along the line y=2x+4. If the length  of of the hypotenuse is 60 find the area of the triangle ABC.

ashutosh kataria
16 Points
3 years ago
The easiest way to solve this question is by shifting the centroid to origin.
Thus now equations of median are y=x and y=2x.
Now the coordiantes of A can be taken as (a,a) and that of B can be taken as (b,2b)
Using centroid formula C(-a-b,-a,-2b)
Equate hypotenuse length equal to 60 get one equation. Second equation comes from slope of AC and BC product is -1.Solving both the equations you will get ab=(-800/3).
Find out area of triangle using all three co-ordinates. Area=3/2 (ab)
=400