Q10 of 95 Page 6

In the given figure, DE || BC. If DE = 5 cm, BC =10 cm and ar(ΔADE) = 20 cm2, find the area of ΔABC.

Given: DE || BC

DE = 5cm, BC = 10cm and area (ADE) =20 sq. cm


In ABC andADE


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


Corresponding angles are equal]


∠C = ∠E [∵ DE || BC and AB 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) = 20×4


⇒ ar (ABC) = 80cm2


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