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A polygon has 44 diagonals. The number of its sides is
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1541 Upvotes
Verified Answer
The correct answer is:
11
Hints: ${ }^n \mathrm{C}_2-n=44$
$$
\begin{aligned}
& \frac{n(n-1)}{2}-n=44 \\
& n\left[\frac{n-1}{2}-1\right]=44 \\
& n(n-3)=88 \\
& n(n-3)=11 \times 8 \\
& n=11
\end{aligned}
$$
$$
\begin{aligned}
& \frac{n(n-1)}{2}-n=44 \\
& n\left[\frac{n-1}{2}-1\right]=44 \\
& n(n-3)=88 \\
& n(n-3)=11 \times 8 \\
& n=11
\end{aligned}
$$
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