A) 10.5 cm
B) 21 cm
C) 31.5 cm
D) Cannot be determined as data is insufficient
Correct Answer: C
Solution :
Given that, \[PQ=4\,\,\text{cm,}\] \[QR=3\,\,\text{cm},\]\[RP=3.5\,\,\text{cm}\] and \[EF=9\,\,\text{cm}\] \[\because \] \[\Delta PQR\sim \Delta DEF\] \[\therefore \] \[\frac{PQ}{DE}=\frac{QR}{EF}=\frac{RP}{FD}\] \[\Rightarrow \]\[\frac{PQ}{DE}=\frac{QR}{EF}\]\[\Rightarrow \]\[\frac{4}{DE}=\frac{3}{9}\] \[\Rightarrow \]\[DE=12\,\,\text{cm}\] and \[\frac{PQ}{DE}=\frac{RP}{FD}\] \[\Rightarrow \] \[\frac{4}{12}=\frac{3.5}{FD}\]\[\Rightarrow \]\[FD=10.5\,\,\text{cm}\] \[\therefore \]Perimeter of \[\Delta DEF=DE+EF+FD\] \[=12+9+10.5=31.5\,\,\text{cm}\]You need to login to perform this action.
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