1. In triagleABC DE ll BC and AD = 1/3AB. Find ar[ADE]/ar[DBCE] Share with your friends Share 1 Manbar Singh answered this Since, DE∥BC, DB is a transversal, then∠ADE = ∠ABC Corresponding anglesSince DE ∥ BC, EC is a transversal,∠AED = ∠ACB Corresponding anglesIn △ ADE and △ ABC,∠ADE = ∠ABC Proved above∠AED = ∠ACB⇒ △ ADE ~ △ ABC AANow, we know that ratio of areas of 2 similar △'s is equal to ratio of the squares of their corresponding sides.Now, ar. △ ADEar. △ ABC = ADAB2⇒ ar. △ ADEar. △ ABC = 132 ∵ AD = 13 AB⇒ ar. △ ADEar. △ ABC = 19 ..............1Now, ar. △ ABC = ar. △ ADE + ar. □ DBCE⇒ 9 ar. △ ADE = ar. △ ADE + ar. □ DBCE⇒ 8 ar. △ ADE = ar. □ DBCE⇒ ar. △ ADEar. □ DBCE = 18 16 View Full Answer