SOLUTION: in a triangle ABC, D and E are two points on sides AB and AC respectively so that DE parallel to BC and AD/DB=2/3.Then, the area of trapezium DECB/the area of triangle ABC is equal

Algebra ->  Triangles -> SOLUTION: in a triangle ABC, D and E are two points on sides AB and AC respectively so that DE parallel to BC and AD/DB=2/3.Then, the area of trapezium DECB/the area of triangle ABC is equal      Log On


   

Question 980769: in a triangle ABC, D and E are two points on sides AB and AC respectively so that DE parallel to BC and AD/DB=2/3.Then, the area of trapezium DECB/the area of triangle ABC is equal to ?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
in a triangle ABC, D and E are two points on sides AB and AC respectively so
that DE parallel to BC and AD/DB=2/3.Then, the area of trapezium DECB/the area
of triangle ABC is equal to ?


We will use three theorems and the fact that ΔADE∽ΔABC.     :

(1).  If p%2Fq=r%2Fs, then p%2F%28p%2Bq%29=r%2F%28r%2Bs%29

(2).  If p%2Fq=r%2Fs, then %28q-p%29%2Fq=%28s-r%29%2Fs

(3).  In two similar triangles, the ratio of their areas is the square
 of the ratio of their sides.

AD%2FDB=2%2F3  given

AD%2F%28AD%2BDB%29=2%2F%282%2B3%29 using (1)

AD%2FAB=2%2F5 simplifying

 using (3)

 using (2)

, simplifying

Edwin