question_answer

 

In the given figure, \[DE||BC\]. If AD = 3 cm, DB = 4 cm and AE = 6 cm, then EC is

A) 8cm

B) 12cm

C) 6cm

D) 4cm

Correct Answer: A

Solution :

 

Given in \[\Delta ABC,DE||BC\],

Let \[EC=x\,cm,\]Then, \[\frac{AD}{DB}=\frac{AE}{EC}\]

[by basic proportionality theorem]

\[\Rightarrow \frac{3}{4}=\frac{6}{x}\]

\[\Rightarrow x=\frac{4\times 6}{3}=8cm\]

\[\therefore EC=8\,cm\].\[\]