Q. A polygon has 54 diagonals. Number of sides of this polygon is
A) 12
B) 15
C) 16
D) 9
Explanation
(a)
$\because\ \ \ \ \ \ \ \frac{n(n - 3)}{2} = 54$
$\Rightarrow \ \ \ \ \ \ n^{2} - 3n - 108 = 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ (n - 12)(n + 9) = 0$
$\Rightarrow \ \ \ \ \ \ \ \ n = 12\ \ \ \ \ \ \ \ \ \ \lbrack\because n \neq - 9\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.