Question

In figure, if DE || BC, find the ratio of ar(ADE) 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