question_answer

\[\Delta ABC\] is such that \[AB=3cm,\] \[BC=2cm\] and \[CA=2.5cm.\] If \[\Delta DEF\tilde{\ }\Delta ABC\] and \[EF=4cm,\] then perimeter of \[\Delta DEF\] is

A)                      \[7.5cm\]        

B)         \[15cm\]         

C)  \[22.5cm\]      

D)         \[30cm\]

Correct Answer: B

Solution :

Since.   \[\Delta DEF\tilde{\ }\Delta ABC\]  [Given]    \[\Rightarrow \] \[\frac{AB}{DE}=\frac{BC}{EF}\] \[\Rightarrow \] \[\frac{3}{DE}=\frac{2}{4}\]\[\Rightarrow \] \[DE=6\,cm\] Also,  \[\frac{AC}{DF}=\frac{BC}{EF}\Rightarrow \frac{2.5}{DF}=\frac{2}{4}\Rightarrow DF=5\,cm\] \[\therefore \] Perimeter of \[\Delta DEF=DE+EF+FD\] \[=6\text{ }cm+4\text{ }cm+5\text{ }cm=15\text{ }cm\]