Question

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

Answer 1

Given: DE || BC

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

In ΔABC and ΔADE

∠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]

∴ ΔABC ~ ΔADE [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.