Question

In figure, if DE || BC, then `(ar(ΔADE))/(ar(DECB)` = ______.

Answer 1

In figure, if DE || BC, then `(ar(ΔADE))/(ar(DECB)` = `underlinebb(1/3)`.

Explanation:

DE = 6 cm, BC = 12 cm

⇒ `(DE)/(BC) = 1/2`

DE || BC so ΔADE ∼ ΔABC; corresponding linear ratio = `1/2`.

Hence `(area(ΔADE))/(area(ΔABC)) = (1/2)^2 = 1/4`.

Area (DECB) = area (ΔABC) – area (ΔADE) 

= `1 - 1/4` 

= `3/4` of area (ΔABC)

Therefore `(ar(ΔADE))/(ar(DECB)) = (1/4)/(3/4) = 1/3`.