Question : In a $\triangle$ABC, DE||BC, D and E lie on AB and AC, respectively. If AB = 7 cm and BD = 3 cm, then find BC : DE.
Option 1: 2 : 3
Option 2: 3 : 2
Option 3: 3.5 : 2
Option 4: 7 : 2
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Correct Answer: 3.5 : 2
Solution : Given: AB = 7 cm BD = 3 cm ∴ AD = 7 – 3 = 4 cm DE || BC ∴ $\angle$ADE = $\angle$ABC $\angle$AED = $\angle$ACB ∴ By AA - similarity theorem, ∆ ADE $\sim$ ∆ ABC $\frac{AB}{AD}=\frac{BC}{DE}$ ⇒ $\frac{7}{4}=\frac{BC}{DE}$ ∴ BC : DE = 3.5 : 2 Hence, the correct answer is 3.5 : 2.
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