10th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    A rectangular garden of length \[(2{{x}^{3}}+5{{x}^{2}}-7)m\]has the perimeter \[(4{{x}^{3}}-2{{x}^{2}}+4)m.\]. Find the breadth of the garden.

    A)  \[(6{{x}^{2}}-9)m\]

    B)  \[(-6{{x}^{2}}+9)m\]   

    C)  \[(2{{x}^{3}}-7{{x}^{2}}+11)m\]                

    D)  \[(6{{x}^{3}}+7{{x}^{2}}+9)m\]               

    Correct Answer: B

    Solution :

    Length of the garden \[=(2{{x}^{3}}+5{{x}^{2}}-7)m\] Perimeter of the garden \[=2\times \](length + breadth)             \[\therefore \]\[4{{x}^{3}}-2{{x}^{2}}+4=2(2{{x}^{3}}+5{{x}^{2}}-7+breadth)\]             \[\Rightarrow \] \[2{{x}^{3}}-{{x}^{2}}+2=(2{{x}^{3}}+5{{x}^{2}}-7)+\] breadth So, breadth of the rectangle \[=2{{x}^{3}}-{{x}^{2}}+2-2{{x}^{3}}-5{{x}^{2}}+7=(-6{{x}^{2}}+9)m\]


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