question_answer

If \[\Delta ABC\] is similar to \[\Delta DEF\]such that BC = 3 cm, EF = 4 cm and area of \[\Delta ABC=54\,c{{m}^{2}},\] then the area of \[\Delta DEF\] is

A) \[78\,c{{m}^{2}}\]                  

B) \[96\,c{{m}^{2}}\]

C) \[54\,c{{m}^{2}}\]                  

D) \[66\,c{{m}^{2}}\]

Correct Answer: B

Solution :

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

\[\therefore \]      \[\frac{\text{Area}\,\text{of}\,\Delta ABC}{\text{Area}\,\text{of}\,\Delta DEF}=\frac{{{(BC)}^{2}}}{{{(EF)}^{2}}}\]

\[\Rightarrow \]   \[\frac{54}{\text{Area}\,\text{of}\,\Delta DEF}=\frac{9}{16}\]

\[\therefore \] Area of \[\Delta DEF=\frac{54\times 16}{9}=96\,c{{m}^{2}}\]