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  4. The number of diagonals in a polygon is 20. The number of sides of the polygon is

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Q. The number of diagonals in a polygon is $20$. The number of sides of the polygon is

WBJEEWBJEE 2011Permutations and Combinations

Solution:

Let $n$ be a side of polygon.
Then, number of diagonals of the polygon
$={ }^{n} C_{2}-n$
$\Rightarrow 20=\frac{n(n-1)}{2}-n$
$\Rightarrow n^{2}-3 n-40=0$
$\Rightarrow (n+5)(n-8)=0$
$\Rightarrow n=8 \,\,\,(\because n$ cannot be negative)