SOLUTION: in triangle abc, ab=16, ac=24, bc=16, and ad is an angle bisector. find the ratio of the area of triangle abd to the triangle acd.

Question 757750: in triangle abc, ab=16, ac=24, bc=16, and ad is an angle bisector. find the ratio of the area of triangle abd to the triangle acd.
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
the angle bisector of an angle of the triangle divides the opposite side with a ratio proportionate to corresponding sides
so here
Bd/CD=AB/Ac .........1
now the ratio of areas=ABD/ACD=[(1/2)BD*h]/[(1/2)CD*h] {h=height of the triangles being same for same vertex}
so ABD/ACD=BD/CD=AB/Ac=16/24=2/3 (use eqn 1 above)
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