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Q. If a polygon of $n$ sides has $275$ diagonals, then $n$ is equal to

EAMCETEAMCET 2007

Solution:

A polygon of $n$ sides has number of diagonals
$=\frac{n(n-3)}{2}=275$ (given)
$\Rightarrow n^{2}-3 n-550 =0$
$\Rightarrow n^{2}-25 n+22 n-550=0$
$\Rightarrow n(n-25)+22(n-25)=0$
$\Rightarrow (n-25)(n+22)=0$
$\Rightarrow n=25,(\because n=-22$ is not possible)