question_answer

\[\Delta ABC\tilde{\ }\Delta DEF\]and the perimeters of \[\Delta ABC\] and \[\Delta DEF\]are 30 cm and 18 cm respectively. If BC = 9 cm, then EF =

A) 6.3cm

B) 5.4cm

C) 7.2cm

D) 4.5cm

Correct Answer: B

Solution :

Given,

\[\Delta ABC\tilde{\ }\Delta DEF\]

\[\therefore \,\,\,\,\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}\]                      … (i)

From eq. (i),

\[\frac{AB+BC+CA}{DE+EF+DF}\]\[=\frac{Perimeter\,of\,\Delta ABC}{Perimeter\,\,of\,\Delta DEF}=\frac{30}{18}\]

Therefore, \[=\frac{Perimeter\,of\,\left( \Delta ABC \right)}{Perimeter\,\,of\,\left( \Delta DEF \right)}=\frac{BC}{EF}\]

\[\Rightarrow \,\,\,\frac{30}{18}=\frac{9}{EF}\]

\[\Rightarrow \,\,\,EF=\frac{18\times 9}{30}=5.4\,\,\,cm\]