10th Class Mathematics Real Numbers Question Bank Real Number

  • question_answer
    Diagonals of a rhombus are \[\left( {{\mathbf{2}}^{\mathbf{5}}}\mathbf{\times 7} \right)\] cm and \[\left( \mathbf{2\times }{{\mathbf{5}}^{\mathbf{2}}}\mathbf{\times }{{\mathbf{7}}^{\mathbf{3}}} \right)\] cm. Express the area of the rhombus in prime factorization form.

    A)  \[2\times 5\times 7\text{ }c{{m}^{2}}\]            

    B)  \[{{2}^{2}}\times {{5}^{2}}\times {{7}^{2}}c{{m}^{2}}\]  

    C)  \[{{2}^{5}}\times {{5}^{2}}\times {{7}^{4}}c{{m}^{2}}\]   

    D)  \[~{{2}^{6}}\times {{5}^{2}}\times {{7}^{4}}c{{m}^{2}}\]

    Correct Answer: C

    Solution :

    (c): Area \[=\frac{1}{2}\times \] Product of diagonals \[=\frac{1}{2}\times \left( {{2}^{5}}\times 7 \right)\times \left( 2\times {{5}^{2}}\times {{7}^{3}} \right)\] \[={{2}^{5}}\times {{7}^{4}}\times {{5}^{2}}\]      


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