Question 8 In figure, if DEIIBC, find the ratio of ar (ΔADE) and ar (ΔDECB).
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Solution
Given, DE || BC, DE= 6cm and BC = 12cm In ΔABC and ΔADE, ∠ABC=∠ADE [corresponding angles] ∠ACB=∠AED [corresponding angles] and ∠A=∠A [common angle] ∴ΔABC∼ΔADE [by AAA similarity criterion] Then, ar(ΔADE)ar(ΔABC)=(DE)2(BC)2 =(6)2(12)2=(12)2 ⇒ar(ΔADE)arΔABC=(12)2=14 Let ar (ΔADE)=k, then ar (ΔABC)=4k Now, ar(DECB)=ar(ABC)−ar(ADE)=4k−k=3k ∴ Required ratio = ar(ADE) : ar(DECB) = k : 3k = 1 : 3