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A polygon has 44 diagonals. Then the number of sides of the polygon are
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Verified Answer
The correct answer is:
11
Number of diagonals of ' $n$ ' sided polygons $={ }^n C_2-n$
$$
\begin{aligned}
& \therefore{ }^n C_2-n=44 \\
& \frac{n !}{2 !(n-2) !}-n=44 \Rightarrow n(n-1)-2 n=88 \\
& \therefore n^2-3 n-88=0 \Rightarrow(n-11)(n+8)=0 \\
& \Rightarrow n=11 \ldots[n \in N]
\end{aligned}
$$
$$
\begin{aligned}
& \therefore{ }^n C_2-n=44 \\
& \frac{n !}{2 !(n-2) !}-n=44 \Rightarrow n(n-1)-2 n=88 \\
& \therefore n^2-3 n-88=0 \Rightarrow(n-11)(n+8)=0 \\
& \Rightarrow n=11 \ldots[n \in N]
\end{aligned}
$$
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