A) 5 cm
B) 7.5 cm
C) 15 cm
D) 18 cm
Correct Answer: C
Solution :
As \[\Delta ABC\sim \Delta DEF\]\[\Rightarrow \]\[\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}\] |
\[\Rightarrow \] But \[\frac{BC}{EF}=\frac{2}{4}=\frac{1}{2}\] |
\[\therefore \] \[DE=2AB=2\times 3=6\,\,\text{cm}\] |
\[DF=2\times AC=2\times 2.5=5\,\,\text{cm}\] |
\[\therefore \]Perimeter of \[\Delta DEF=(6+5+4)=15\,\,\text{cm}\] |
Shortcut method |
\[\frac{\text{Perimeter}\,\,\text{of}\,\,\Delta ABC}{\text{Perimeter}\,\,\text{of}\,\,\Delta DEF}=\]Ratio of corresponding sides |
\[\therefore \] \[\frac{(3+2+2.5)}{\text{Perimeter}\,\,\text{of}\,\,\Delta DEF}=\frac{1}{2}\] |
\[\therefore \] Perimeter of \[\Delta DEF=2\,\,(7.5)=15\,\,\text{cm}\] |
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