Question : ABC is a triangle in which DE || BC and AD : DB = 5 : 4. Then DE : BC is:
Option 1: 4 : 5
Option 2: 4 : 9
Option 3: 9 : 5
Option 4: 5 : 9
Correct Answer: 5 : 9
Solution :
AD : DB = 5 : 4
In $\triangle$ADE and $\triangle$ABC,
$\angle$ADE = $\angle$ABC and $\angle$AED = $\angle$ACB [i.e., corresponding angles in DE || BC]
$\angle$A = $\angle$A [common angle]
⇒ $\triangle$ADE ~ $\triangle$ABC
⇒ $\frac{\text{AD}}{\text{AB}}$ = $\frac{\text{DE}}{\text{BC}}$
⇒ $\frac{5}{5+4}$ = $\frac{\text{DE}}{\text{BC}}$
⇒ $\frac{\text{DE}}{\text{BC}}$ = $\frac{5}{9}$
Hence, the correct answer is 5 : 9.
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