How many sides does a polygon having 27 diagonals have
Asked by admin @ in Math viewed by 292 People
A polygon has 27 diagonals. How many sides does it have???
Answered by admin @
Number of sides in a polygon = n(n - 3)/2
Here, n = sides of the polygon.
Given :-
Diagonals = 27
To find :-
Number of sides.
Solution :-
n(n - 3)/2 = 27
n² - 3n = 27 x 2
n² - 3n = 54
n² - 3n - 54 = 0
Solving for n :-
n² - 3n - 54 = 0
(n − 9)(n + 6) = 0
n = 9 or n = -6
Number of sides cannot be negative, therefore there are 9 sides in the polygon.
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