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If median of triangle are 5cm,6cm,7cm then find the area

sanatan sharma
26 Points
9 years ago

let the required triangle be ABC and the medians  AD = 5 , BE = 6 , CF = 7

let the centroid be O therefore by 2:1 property of centroid DO = 5/3  ,  BO = 4 and CO = 14/3

now consider triangle BOC and drop a perpendicular on BC and mark the point on which it falls be G

now BD = x  and DC = x , BG = x-y and GD = y

appyling pythagoras theoem

16 - (x-y)2 = (14/3)2 - (x+y)2                       and

(5/3)2 - y2 = (14/3)2 - (x+y)2

solve the two equations to get x = (√145)/3  and y = 13/(3√145)

now perpendicular OG can be calculated which will come out as √(384/145)

in triangle BOC base BC =2x = 2(√145)/3    and height OG = √(384/145)

area of triangle  BOC = (8√6)/3

therefore the area of triangle ABC = 3 ( area of triangle BOC)

= 8√6