10th Class Mathematics Triangles Question Bank Case Based (MCQs) - Triangles

  • question_answer
    In the given figure, the side PQ of a right triangle \[\Delta PQR\]where \[\text{OP}=\text{6 cm},\] \[\text{OR}=\text{8 cm}\] and \[\text{QR}=\text{26 cm},\]is :

    A) \[21\,cm\]

    B) \[23\,cm\]

    C) \[24\,cm\]

    D) \[36\,cm\]

    Correct Answer: C

    Solution :

    Applying Pythagoras theorem in triangle POR, we get,    
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,PR=10cm\]
    Now, the apply Pythagoras theorem in triangle PQR.      
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,{{26}^{2}}=P{{Q}^{2}}+{{10}^{2}}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,P{{Q}^{2}}={{26}^{2}}-{{10}^{2}}=676-100=576\]
    Therefore, \[\text{PQ}=\text{24 cm}\].     
    So, option [c] is correct

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