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, \[=\frac{Perimeter\,of\,\left( \Delta ABC \right)}{Perimeter\,\,of\,\left( \Delta DEF \right)}=\frac{BC}{EF}\] |
\[\Rightarrow \,\,\,\frac{30}{18}=\frac{9}{EF}\] |
\[\Rightarrow \,\,\,EF=\frac{18\times 9}{30}=5.4\,\,\,cm\] |
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