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.
Answers
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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