If in a regular polygon the number of diagona | vedclass

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(A) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n - 3)}{2}$.Given that the number of diagonals is $54$,we hav

Vedclass · Accepted Answer

$12$

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(A) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n - 3)}{2}$.Given that the number of diagonals is $54$,we have:$\frac{n(n - 3)}{2} = 54$$n(n - 3) = 108$$n^2 - 3n - 108 = 0$Factoring the quadratic equation:$n^2 - 12n + 9n - 108 = 0$$n(n - 12) + 9(n - 12) = 0$$(n - 12)(n + 9) = 0$This gives $n = 12$ or $n = -9$.Since the number of sides $n$ must be a positive integer,we have $n = 12$.

If in a regular polygon the number of diagonals is $54$,then the number of sides of this polygon is

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