question_answer

If\[\Delta ABC\tilde{\ }\Delta POR\], AB = 6.5 cm, PQ = 10.4cm and perimeter of \[\Delta ABC=60\,cm\], the perimeter of \[\Delta PQR\]is

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.