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