Question

a polygon has 27 diagonal. how many sides does it have​

Answer 1

Answer:

9

Step-by-step explanation:

Formula to calculate the diagonal of a polygon = n(n-3)/2 when n is the side of the polygon.

So,

n(n-3)/2 = 27

or,

n(n-3) = 54

or,

n²-3n-54 = 0

or,

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

or,

n = 9 , -6

or,

n = 9 [∵ Side of Polygon should be in +ve integers.]

Answer 2

no of diagonals if a polygon of 'n' is given by n(n-3)/2

given it has 27 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...but side can't be negative..

hence n=9..i.e, it is has 9 sides..