Question

In a ∆ABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then Area (∆ ADE) : Area (◻BCED) =

(a) 3 : 4
(b) 9 : 16
(c) 3 : 5
(d) 9 : 25

Answer 1

Given: In ΔABC, D is on side AB and point E is on side AC, such that BCED is a trapezium. DE: BC = 3:5.

To find: Calculate the ratio of the areas of ΔADE and the trapezium BCED.

In ΔADE and ΔABC,

$$\begin{gathered} \angle \mathrm{ADE}=\angle \mathrm{B}\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{A}=\angle \mathrm{A}\left(\mathrm{Common}\right) \\ \therefore ∆\mathrm{ADE}~∆\mathrm{ABC}\left(\mathrm{AA}\mathrm{Similarity}\right) \end{gathered}$$

We know that

Let Area of ΔADE = 9x sq. units and Area of ΔABC = 25x sq. units

Now ,

Hence the correct answer is.