In ΔABC, D and E are the points on sides AB and AC, respectively, such that DE || BC. If DE : BC is 4 : 5, then (Area of ΔADE) : (Area of quadrilateral DECB) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 16 : 9.
If all three angles of 2 triangles are equal, then these two triangles are similar triangles.
And
(Area of triangle1/ Area of triangle2) = (Side12/Side22)
Given
DE || BC and DE : BC = 4 : 5
Area of ∆ADE/Area of ∆ABC = (DE/BC)2
⇒ Area of ∆ADE/Area of ∆ABC = (4/5)2 = 16 : 25
In the figure:
Area of quadrilateral DECB = Area of ∆ABC – Area of ∆ADE
(Area of ∆ADE) : (Area of quadrilateral DECB) = 16 : (25 – 16) = 16 : 9