Question

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

Answer 1

formula is {n(n-3)}/2
where n=no. of sides of the polygon.

so according to question:
27={n(n-3)}/2
=>54=n^2-3n
solving this equation we get n=9

hence no. of sides of the polygon=9

Answer 2

in a  polygon no of daignols equal to C(n,2) -n where n is no of sides
therefore 27 = C(n,2)
$n_{C} _{2}= 27$
n(n-1)/2  -n =27
n∧2 -3n -54 =0
from above we get two values of n -6 and 9
no of sides cant we negative so 9 is the answer.
or you can simply solve by
n(n-3)/2 = no of daigonals