A) 65cm
B) 96cm
C) 60cm
D) 104cm
Correct Answer: B
Solution :
Given, \[\Delta ABC\sim \Delta PQR\] with AB = 6.5 cm and PQ = 10.4 cm |
Since, \[\Delta ABC\sim \Delta PQR\] |
\[\therefore \,\,\,\,\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=\frac{6.5}{10.4}=\frac{65}{104}\] |
[\[\because\] corresponding sides of similar triangles are proportional] |
\[\Rightarrow \,\,AB=\frac{65}{104}PQ\],\[BC=\frac{65}{104}QR\],\[AC=\frac{65}{104}PR\] |
Also given, perimeter of \[\Delta ABC=60\] |
\[\therefore \,\,\,\,AB+BC+AC=60\] |
\[\Rightarrow \,\,\frac{65}{104}\left( PQ+QR+PR \right)=60\] |
\[\Rightarrow \,\,\,PQ+QR+PR=\frac{60\times 104}{65}=96\,cm\] |
Hence, perimeter of \[\Delta \,PQR\] is 96 cm. |
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