Question

In a ΔABC, DE ║ BC. If DE = 3 cm, BC = 6 cm and area (ΔADE) = 15 sq. cm, then find the area of ΔABC.

Answer 1

Answer:

• 60 cm² is the area of ΔABC.

Explanation:

In ΔABC,

DE║BC [Given]

Now, in ΔADE and ΔABC,

∠D = ∠B [Corresponding angles]

∠E = ∠C [Corresponding angles]

∴ ΔADE ~ ΔABC [By AA similarity]

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

∴ ar(ΔADE)/ar(ΔABC) = DE²/BC² = 3²/6²

[Given DE = 3 cm and BC = 6 cm]

15/ar(ABC) = 9/36

∴ ar(ΔABC) = 15 × 36/9 = 60

Hence, the area of ΔABC is 60 cm².