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10th Class Mathematics Triangles Question Bank MCQs - Triangles

  • question_answer
    \[\Delta ABC\tilde{\ }\Delta PQR\] such that \[ar(\Delta ABC)=4ar(\Delta PQR)\]. If \[BC=12\,cm,\]then \[QR=\]

    A) 9 cm

    B) 10 cm

    C) 6 cm

    D) 8 cm

    Correct Answer: C

    Solution :

    [c] Since   \[\Delta ABC\tilde{\ }\Delta PQR\]
    \[\therefore \,\,\,\,\,\,\frac{ar(\Delta ABC)}{ar(\Delta PQR)}=\frac{B{{C}^{2}}}{Q{{R}^{2}}}\]
    \[\Rightarrow \,\,\,\frac{4ar(\Delta PQR)}{ar(\Delta PQR)}=\frac{{{12}^{2}}}{Q{{R}^{2}}}\]
    [Given, \[ar(\Delta ABC)=4ar(\Delta PQR)\]]
                \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,Q{{R}^{2}}=\frac{144}{4}=36\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,QR=6\,cm\]


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