Question

A polygon has $44$ diagonals. The number of its sides are

• A. 9
• B. 8
• C. 11
• D. 7

Answer 1

Answer: (C)

Let $n$ be the number of sides of given polygon.
$\therefore$ Polygon with $n$ sides $=\frac{n(n-3)}{2}$ diagonal
$\Rightarrow \frac{n(n-3)}{2}=44$ [given]
$\Rightarrow n^2-3n=88$
$\Rightarrow n^2-3n-88=0$
$\Rightarrow n(n-11)+8(n-11)=0$
$\Rightarrow (n+8)(n-11)=0$
$\Rightarrow n+8=0$ or $n-11=0$
$\Rightarrow n=-8$ or $n=11$
But side cannot be negative.
$\therefore n=11$