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7th Class Mathematics Perimeter and Area Question Bank Perimeter and Area

  • question_answer
    In the following figure, ABCD is a   parallelogram. \[DL\bot AB\] and \[AB=13\text{ }cm=AD\] . If the area of parallelogram is \[156\text{ }c{{m}^{2}},\]find AL.

    A)  \[5\,\,cm\]  

    B)                         \[6\,\,cm\]

    C)  \[7\,\,cm\]        

    D)         \[8\,\,cm\]

    Correct Answer: A

    Solution :

     We have, area \[=156\text{ }c{{m}^{2}}\] \[\Rightarrow \] \[b\times h=156\] \[AB\times DL=156\] \[DL=\frac{156}{AB}=\frac{156}{13}=12\,cm\] In right \[\Delta \,\,ADL,\] \[A{{D}^{2}}=D{{L}^{2}}+L{{A}^{2}}\] \[A{{L}^{2}}=A{{D}^{2}}-D{{L}^{2}}={{13}^{2}}-{{12}^{2}}=25\]  \[\therefore \]  \[AL=\sqrt{25}=5\,cm\]


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