Question

In figure, if DE || BC, find the ratio of ar(ΔADE) and ar (DECB).

Answer 1

Given, DE || BC, DE = 6 cm and BC = 12 cm

In ΔABC and ΔADE,

∠ABC = ∠ADE   .......[Corresponding angle]

∠ACB = ∠AED   .....[Corresponding angle]

And ∠A = ∠A   .....[Common side]

∴ ΔABC ∼ ΔAED   .....[By AAA similarity criterion]

Then, `(ar(ΔADE))/(ar(ΔABC)) = (DE)^2/(BC)^2`

= `(6)^2/(12)^2 = (1/2)^2`

⇒ `(ar(ΔADE))/(ar(ΔABC)) = (1/2)^2 = 1/4`

Let ar(ΔADE) = k, then ar(ΔABC) = 4k

Now, ar(DECB) = ar(ABC) – ar(ΔADE) = 4k – k = 3k

∴ Required ratio = ar(ADE) : ar(DECB) = k : 3k = 1 : 3