In triangle ABC, the point D lies on AB and E lies on AC so that DE is parallel to BC and AD : DB = 2 : 3. Find the ratio of the area of triangle ADE to the area of trapezium DBCE.

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4:21. DE ∥ BC makes triangle ADE similar to triangle ABC with AD : AB = 2 : 5, so their areas are in the ratio 4 : 25. Taking [ABC] as 25 parts, [ADE] = 4 parts and the trapezium = 25 − 4 = 21 parts. Ratio = 4 : 21.

In triangle ABC, the point D lies on AB and E lies on AC so that DE is parallel to BC and AD : DB = 2 : 3. Find the ratio of the area of triangle ADE to the area of trapezium DBCE.

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