D and E are points on the sides AB and AC respectively of ang ABC such that DE is parallel to BC and...........

Quantitative Aptitude (CGL) Coordinate Geometry

D and E are points on the sides AB and AC respectively of ∠ABC such that DE is parallel to BC and AD:DB = 4:5, CD and BE intersect each other at F. Then the ratio of the areas of ∠DEF and ∠CBF

16:25

16:81

81:16

4:9

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Explanation:

?ADE∼?ABC
∴∠D=∠B
&∠E=∠C
∠A is common.
So,
AD/AB=AE/AC=DE/BC=4/9
Now, In?DEF and ?BFC
∠D=∠C and
∠B=∠E
So, ?DEA∼ ?BFC
In similar triangles ratio of areas is equal to the ratio of square of corresponding sides.
(area of ?DEF)/(area of ?BFC)=DE^2/BC^2
=4^2/9^2=16/81