In fig., DE||BC, AD=1cm and BD=2cm. What is the ratio of the ar(ΔABC) to the ar(ΔADE)?<p></p>

Consider the ΔABC, ΔADE
DE||B ⇒ ∠ADE = ∠ABC
∠AED = ∠ACB
∠DAE = ∠BAC
So, the triangles are similar
⇒ar(ΔABC)/ar(ΔADE) = (AB/AD)²
(AB = AD + DB = 1 + 2 = 3cm)
⇒(3/1)² = 9
So the Ratio is 9:1

Eduprobe

Question:

In fig., DE||BC, AD=1cm and BD=2cm. What is the ratio of the ar(ΔABC) to the ar(ΔADE)?

Solution: