Question

In the given figure, DE || BC and DE : BC = 4 : 5. Calculate the ratio of the areas of ΔADE and the trapezium ΔCEDB.

Answer 1

It is given that DE || BC and DE : BC = 4 : 5

Let ∆ ADE and ∆ABC

∠ADE = ∠ABC [corresponding angles]

∠AED = ∠ACB [corresponding angles]

∴ ∆ ADE ~ ∆ABC [by AA similarity]

We know that the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.