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10th Class Mathematics Triangles Question Bank MCQs - Triangles

  • question_answer
    The areas of two similar triangles are \[25c{{m}^{2}}\]and \[36c{{m}^{2}}\].If the median of the smaller triangle is \[\text{1}0\text{ cm},\] then the median of the larger triangle is:

    A) \[12cm\]

    B) \[15cm\]

    C) \[10cm\]

    D) \[18cm\]

    Correct Answer: A

    Solution :

    [a] Let the median of the larger triangle be \[x\,cm.\]We know, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.       
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{25}{36}={{\left( \frac{10}{x} \right)}^{2}}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}=\frac{100\times 36}{25}=144\Rightarrow x=12\,cm\]


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