Q6 of 95 Page 6

In the figure DE || BC. If DE = 4 cm, BC = 8 cm and area (ΔADE) = 25 sq. cm, find the area of ΔABC.

Given: DE || BC

DE = 4cm, BC = 8cm and area (ADE) =25 sq. cm


In ABC andADE


∠B = ∠D [∵ DE || BC and AB is transversal,


Corresponding angles are equal]


∠C = ∠E [∵ DE || BC and AC is transversal,


Corresponding angles are equal]


∠BAC =∠DAE [common angle]


∴ ABC ~ADE [by AAA similarity]


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



[given]




⇒ ar(ABC) = 25×4


⇒ ar (ABC) = 100cm2


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