Q. If a polygon has 44 diagonals, then the number of its sides are
A) 11
B) 7
C) 8
D) None of these
Explanation
(a)
Let $n$ be the number of diagonals of a polygon.
Then, $\ ^{n}C_{2} - n = 44$
$\Rightarrow \frac{n(n - 1)}{2} - n = 44$
$\Rightarrow n^{2} - 3n - 88 = 0$
$\Rightarrow n = - 8\ or\ 11$
$\therefore n = 11$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.