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

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Aicharya · Accepted Answer

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

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

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