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7th Class Mathematics Mensuration Question Bank Mensuration

  • question_answer
    If all the sides of a triangle be increased by 200 per cent, what is the corresponding increase in its area?

    A) 300%                          

    B) 400%

    C) 600%                          

    D) 800%

    Correct Answer: D

    Solution :

        Let sides are a, b, c. So new sides are 3a, 3b, 3c and new perimeter = 3s Original area \[=\sqrt{s(s-a)\,(s-b)\,(s-c)}=K\] \[\therefore \] New area \[=\sqrt{3s(3s-3a)\,(3s-3b)\,(3s-3c)}\] \[=\sqrt{3\times 3\times 3\times 3s(s-a)(s-b)(s-c)}\] \[=9\left( \sqrt{s(s-a)(s-b)(s-c)} \right)=9K\] Increased area\[9K-K=8K\] \[\therefore \] % increase = 800%.


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