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If a polygon has 20 diagonals, then what is the number of sides?
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Verified Answer
The correct answer is:
8
Number of diagonals $=\frac{n(n-3)}{2}$ where $n$ is the number of sides of polygon
$\therefore \quad 20=\frac{n(n-3)}{2}$
$\Rightarrow \quad 40=n^{2}-3 n$
$\Rightarrow \quad n^{2}-3 n-40=0$
$\Rightarrow \quad n^{2}-8 n+5 n-40=0$
$\Rightarrow \quad(n-8)(n+5)=0$
$\Rightarrow \quad \quad n-8=0, n+5=0$
$\therefore$ since, thenumber of diagonals, $n$ cannot benegative.
$\Rightarrow$
$n=8$
$\therefore \quad 20=\frac{n(n-3)}{2}$
$\Rightarrow \quad 40=n^{2}-3 n$
$\Rightarrow \quad n^{2}-3 n-40=0$
$\Rightarrow \quad n^{2}-8 n+5 n-40=0$
$\Rightarrow \quad(n-8)(n+5)=0$
$\Rightarrow \quad \quad n-8=0, n+5=0$
$\therefore$ since, thenumber of diagonals, $n$ cannot benegative.
$\Rightarrow$
$n=8$
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