Q. If a polygon of $n$ sided has 275 diaginals, then $n$ is equal to
A) 25
B) 35
C) 20
D) 15
Explanation
(a)
A polygon of $n$ sides has number of diagonals
$= \frac{n(n - 3)}{2} = 275$ [given]
$\Rightarrow \ \ \ \ \ \ n^{2} - 3n - 550 = 0$
$\Rightarrow \ \ \ \ (n - 25)(n + 22) = 0$
$\Rightarrow \ \ \ \ \ n = 25$ $\lbrack\because\ \ \ \ n \neq - 22\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.