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Railways Sample Paper RRB (Assistant Loco Pilot & Technician) Sample Test Paper-10

  • question_answer
    In the figure, \[\Delta PQR\,\,\,AB||QR.\] If AB is 3 cm, PB is 2 cm and PR is 6 cm, find the length of QR.

    A)  8cm                            

    B)  9cm

    C)  10cm              

    D)       7cm

    Correct Answer: B

    Solution :

     \[AB||QR\] (given) \[\therefore \]         \[\angle PAB=\] Corresp. \[\angle PQR\]              \[\angle PBA=\] Corresp.  \[\angle PRQ\]             \[\angle PAB\] is common to \[\Delta PAB\]                                          and \[\angle PQR\]              \[\therefore \] \[\Delta PAB\,\,\tilde{\ }\,\Delta PAB\] (AAAsimilarity theorem) \[\therefore \] \[\frac{PB}{PR}=\frac{AB}{QR}\] \[\Rightarrow \]\[\frac{2}{6}=\frac{3}{QR}\] \[\Rightarrow \]\[2QR=18\]        \[QR=9cm.\]


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