question_answer

It is given that \[\Delta ABC\tilde{\ }\Delta EDF\]such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. The lengths of the remaining sides of the triangles is

A) 16.8 cm, 6.25 cm

B) 16.8 cm, 12cm

C) 12 cm, 6.25cm

D) None of these

Correct Answer: A

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.