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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    A polygon has 54 diagonals. Number of sides of this polygon is:

    A)  12                         

    B)         15

    C)  16                         

    D)         9

    E)  14

    Correct Answer: A

    Solution :

    \[\frac{n(n-3)}{2}=54\] \[\Rightarrow \]               \[{{n}^{2}}-3n-108=0\] \[\Rightarrow \]               \[{{n}^{2}}-12n+9n-108=0\] \[\Rightarrow \]               \[n(n-12)+9(n-12)=0\] \[\Rightarrow \]               \[(n-12)(n+9)=0\] \[\Rightarrow \]               \[n=12\]                               \[(\because n\ne -9)\]


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