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

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) (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 , then 

(2).  If , then 

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

  given

 using (1)

 simplifying

 using (3)

 using (2)

, simplifying

Edwin

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