Question

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

Answer 1

Let n be the number of vertices of the polygon.
then there are n  sides.

N = number of  all connections between all the vertices = 
${}^nC_2$
N = n(n-1)/2

Number of diagonals =  N - n = n (n - 3)/2    =  27  given
           n²  - 3 n  - 54 = 0
        (n - 9) (n + 6) = 0
           n = 9

so there are  9 sides and 9 vertices

Answer 2

Answer:

9

Step-by-step explanation:

n(n-3)/2 = 27

n(n-3) = 54

n2 - 3n = 54

n2-9n+6n = 54

n(n-9)+6(n-9)=54

n = -6 or 9

excluding the negative

n = 9

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