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


Given,

DE || BC,


DE = 6 cm and BC = 12 cm


In ∆ABC and ∆ADE,


ABC = ADE [corresponding angle]


ACB = AED [corresponding angle]


And


A = A [common side]


∆ABC ∆AED [by AAA similarity criterion]


Then,


By property of area of similar triangle,



Let area (∆ADE) = k,


Then area (∆ABC) = 4k


Now,


Area (DECB) = area (ABC) – area (ADE) = 4k – k = 3k


Required ratio = area (ADE) : area (DECB) = k : 3k = 1:3


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