question_answer

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

A)  66\[c{{m}^{2}}\]    

B)  78\[c{{m}^{2}}\]

C)  96\[c{{m}^{2}}\]      

D)  54\[c{{m}^{2}}\]

Correct Answer: C

Solution :

\[\Delta ABC\tilde{\ }\Delta DEF\] \[\therefore \] \[\frac{\Delta ABC}{\Delta DEF}=\frac{{{3}^{2}}}{{{4}^{2}}}\Rightarrow \frac{54}{\Delta DEF}=\frac{9}{16}\] \[\Rightarrow \,\,\Delta DEF=\frac{16\times 54}{9}=96\,sq.\,cm.\]