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Given $\frac{A D}{A B} = \frac{2}{3}$ in triangle ABC with DE || BC, the ratio of the area of triangle ADE to the area of trapezium DBCE is ____.

Class 10Basic Proportionality TheoremGeometry — Similarity

A4 : 5
B2 : 3
C4 : 9
D5 : 4

Step-by-Step Solution

\frac{Area ADE}{Area ABC} = (\frac{2}{3})^{2} = \frac{4}{9}

. Trapezium = ABC - ADE = 9 - 4 = 5 parts. ADE : trapezium = 4 : 5.

Answer: A) 4 : 5

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