Question

In Triangle ABC, D and E are points on sides AB and AC respectively, such that AD:DB=5:4 and DE is parallel to BC. DC and BE intersect at F. find Area of triangle DEF/Area of triangle CBF.

Answer 1

The ratio of areas of triangles is 25 : 81

Explanation:

As 
∠D=∠B (Correesponding angle)
∠E = ∠C ( " )
∠A = ∠A  (Common) 
△ADE∼△ABC (By AAA)

In △DEF and △BFC
∠D=∠C (Alternate interior angle)
∠B=∠E ( " )
△DEA ∼ △BFC
Two triangles are similar ratio of areas is equal to the ratio of square of corresponding sides.
than