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CLAT Sample Paper CLAT Sample Paper-6

  • question_answer
    In the figure given below, \[QA\] and \[PB\] are perpendiculars to \[AB.\] If \[AO=15\,cm,\] \[BO=9\,cm,\] \[PB=\,12\,cm,\] find \[AQ\].

    A)  10 cm

    B)  12 cm

    C)  18 cm   

    D)  20 cm

    Correct Answer: D

    Solution :

    In \[\Delta \,AOQ\] and \[\Delta \,BOP,\] \[\angle 1=\angle 2\]   (vertically opposite angles) \[\angle 3=\angle 4\]                  (each 90°) \[\therefore \] \[\Delta AOQ\sim \Delta BOP\]    (AA similarity criterion)  \[\therefore \] \[\frac{AO}{BO}=\frac{AQ}{BP}\] (corresponding sides of similar triangles) \[\Rightarrow \] \[\frac{15}{9}=\frac{AQ}{12}\Rightarrow \,\frac{5}{1}=\frac{AQ}{4}\] \[\Rightarrow \] \[AQ=20\,cm\]


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