Q. 105.0( 1 Vote )

# 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 and ADE

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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