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SSC Sample Paper Mock Test-9 SSC CGL Tear-II Paper-1

  • question_answer
    In \[\Delta PQR,\]PQ = 4 cm, QR = 3 cm and RP = 3.5 cm. \[\Delta DEF\] is similar to \[\Delta PQR.\] If EF = 9 cm, then what is the perimeter to\[\Delta DEF\]?

    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 \[\Delta DEF=DE+EF+FD\] \[=12+9+10.5=31.5\,\,\text{cm}\]


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