Question

If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :

• A. 10
• B. 12
• C. 9
• D. 6

Answer 1

Answer: (B)

Number of diagonal $= 54$
$\Rightarrow \frac{n\left(n-3\right)}{2}=54$
$\Rightarrow n^{2}-3n-108=0$
$\Rightarrow n^{2}-12n+9n-108 =0$
$\Rightarrow n\left(n- 12\right)+9\left(n-12\right) = 0$
$\Rightarrow n=12,-9$
$\Rightarrow n=12 \left(\because n\ne-9\right)$