polygon has 27 diagonals. How many sides does it have?

1.	polygon has 27 diagonals. How many sides does it have?
Answer» The formula for the no. of diagonals of a ’n' sided polygon is n(n-3)/2 . It works for triangle (0 diagonals) , quadrilateral (2 diagonals) , pentagon (5 diagonals) and for every another polygon. Let's come to the problem. No. Of diagonals = n(n-3)/2 = 27 n(n-3) = 54 n^2 - 3n -54 = 0 n^2 - 9n + 6n - 54 = 0 n(n-9) + 6(n-9) = 0 (n-9)(n+6) = 0 n = 9, -6 (excluding -6) n = 9 The polygon has 9 sides. It is a Nonagon. why there is single n and -6 excluded it has seven sides mean poly means seven

Answer»

The formula for the no. of diagonals of a ’n' sided polygon is n(n-3)/2 .

It works for triangle (0 diagonals) , quadrilateral (2 diagonals) , pentagon (5 diagonals) and for every another polygon.

Let's come to the problem.

No. Of diagonals = n(n-3)/2 = 27

n(n-3) = 54

n^2 - 3n -54 = 0

n^2 - 9n + 6n - 54 = 0

n(n-9) + 6(n-9) = 0

(n-9)(n+6) = 0

n = 9, -6

(excluding -6)

n = 9

The polygon has 9 sides.

It is a Nonagon.

why there is single n and -6 excluded

it has seven sides mean poly means seven

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