Question

A farmer has distributed his land amongst his son and daughter as given in the figure. Part I was given to his
daughter and Part II was given to his son.

If AB = 10 m, BC = 35 m and AC = 30 m and BD = DC, then check whether the distribution of land between
son and daughter are equal.
​

Answer 1

Given :   AB = 10 m, BC = 35 m and AC = 30 m and BD = DC

To Find : whether the distribution of land between son and daughter are equal.​

Solution:

BD = DC  

Hence D is mid point of BC

=> AD is median of triangle

Median divides triangle in two equal area hence  

Area of ΔABD = Area of  ΔACD

Hence distribution of land between son and daughter are equal.​

Another method :

Draw AM  ⊥ BC

Area of triangle ABD = (1/2) BD * AM

Area of triangle ACD = (1/2) CD * AM

BD = CD

Hence (1/2) BD * AM  =  (1/2) CD * AM

=> Area of triangle ABD =   Area of triangle ACD

on more method

let say ∠ADB = α   then ∠ADC = 180° - α  ( linear pair)

area of ΔABD  = (1/2) AD * BD Sin α

area of ΔACD  = (1/2) AD * CD Sin (180° - α)

BD = CD  and Sin α = (180° - α)

Hence area of ΔABD  = area of ΔACD

the distribution of land between son and daughter are equal.​

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