Question

in triangle abc ,e is the mid p.t of median AD .show that ar.( BED)= 1/4th are.(ABC).

Answer 1

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal area.

∴ Area (ΔABD) = Area (ΔACD)

⇒Area (ΔABD ) = (½) area (Δ ABC) ------------(1)

In ΔABD, E is the mid-point of AD.

Therefore, BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

Area (ΔBED) = (1/2)Area (ΔABD)

Area (ΔBED) = (½ ) x(1/2) Area (ΔABC)         [From (1)]

∴ Area (ΔBED) = (1/4)Area (ΔABC).


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Answer 2

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal area.

∴ Area (ΔABD) = Area (ΔACD)

⇒Area (ΔABD ) = (½) area (Δ ABC) ------------(1)

In ΔABD, E is the mid-point of AD.

Therefore, BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

Area (ΔBED) = (1/2)Area (ΔABD)

Area (ΔBED) = (½ ) x(1/2) Area (ΔABC)         [From (1)]

∴ Area (ΔBED) = (1/4)Area (ΔABC).



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