D and E are the points on the sides AB and AC respectively of a triangle ABC such that DE||BC and divides a triangle ABC into two parts , equal in area . Find BD/AB
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As triangle ADE ~ ABC
AD/AB = DE/BC
8/8+12 = DE/BC
8/20 = DE/BC
2/5 = DE/BC
BC = 5/2 DE
AD = 6 cm; BD = 9 cm
AE = 8 cm and CE = 12 cm
Now we have:
AD/BD = 6/9 = 2/3
AE/CE = 8/12 = 2/3
So AD/BD = AE/CE
We know that if a line intersects any two sides of a triangle in equal ratio then the line is parallel to the third side.
DE = BC
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