Correct Answer - Option 1 : 30
Given:
The number of diagonals of a 'n' sided polygon is 405.
Formula used:
Number of diagonal in the polygon = a(a – 3)/2
Where,
a → Number of sides in the polygon
Calculation:
n(n - 3)/2 = 405
⇒ n2 - 3n - 810 = 0
⇒ n2 - 30n + 27n - 810 = 0
⇒ n(n - 30) + 27(n - 30) = 0
⇒ (n + 27) (n - 30) = 0
⇒ n = 30 and - 27
But n can't be - 27 as it is negative.
so, n = 30
∴ value of n is 30
