A polygon has 189 diagonals then how many sides does it have?
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The number of diagonals in a polygon are given by the formula
= n(n-3)/2
where n is the number of sides of the polygon.
So,
189 = n(n-3) / 2
n^2 - 3n = 378
n^2 - 3n - 378 = 0
n^2 - 21n + 18n - 378 = 0
n ( n - 21) + 18 ( n - 21 ) = 0
n = 21 , -18
So as the no. of sides cannot be negative so the number of sides of a polygon having 189 diagonals has 21 sides.
= n(n-3)/2
where n is the number of sides of the polygon.
So,
189 = n(n-3) / 2
n^2 - 3n = 378
n^2 - 3n - 378 = 0
n^2 - 21n + 18n - 378 = 0
n ( n - 21) + 18 ( n - 21 ) = 0
n = 21 , -18
So as the no. of sides cannot be negative so the number of sides of a polygon having 189 diagonals has 21 sides.
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