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Math Help - Looking for a polygon with given diagonals...

  1. #1
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    Looking for a polygon with given diagonals...

    The formula for getting the number of diagonals of a certain polygon is:

    N (N-3) / 2

    where n stands for the polygon..

    But here's the question:

    What kind of polygon has 54 diagonals?

    I tried to manipulate the formula as in reciprocated it in this form:

    54 divided by the difference of 54 and 3 then multiply the quotient by two

    The answer I obtained is 2.11

    Please help me...Please teach me how to manipulate a formula..I also tried to use the triangle method but it doesn't work...
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  2. #2
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    Number of diagonalizes is 54.

    54 = \frac{n(n-3)}{2}

    108 = n(n-3)

    108 = n^2 - 3n

    n^2 - 3n - 108 = 0

    Solve the quadratic to find n.
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  3. #3
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    Another way to solve besides using the quadratic equation is to notice that

    108=2\cdot2\cdot3\cdot3\cdot3

    We are looking for two divisors of 108 whose product is 108 and whose difference is 3. Notice that 108=(4*3)*(3*3) and that 4*3 and 3*3 differ by 3.
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  4. #4
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    Thank you for the replies...I really appreciate it..
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