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Question:

In Fig., (i) and (ii), DE||BC. Find EC in (i) and AD in (ii).

Solution:

(i) Given : DE||BC in △ABC, Using Basic proportionality theorem, ∴AD/DB = AE/EC ⇒1.5/3 = 1/EC ⇒EC = 3/1.5 EC = 3 × 10/15 = 2cm EC = 2cm (ii) In △ABC, DE||BC (Given) Using Basic proportionality theorem, ∴AD/DB = AE/EC ⇒AD/7.2 = 1.8/5.4 ⇒AD = 1.8 × 7.2/5.4 = 18/10 × 72/10 × 10/54 = 24/10 ⇒AD = 2.4cm So, AD = 2.4cm