Question

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

Answer 1

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