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
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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