Question

A polygon has 54 diagonals. Number of sides of this polygon is:

• A. 12
• B. 15
• C. 16
• D. 9
• E. 14

Answer 1

Answer: (A)

$\frac{n(n-3)}{2}=54$ $\Rightarrow$ $n^2-3n-108=0$ $\Rightarrow$ $n^2-12n+9n-108=0$ $\Rightarrow$ $n(n-12)+9(n-12)=0$ $\Rightarrow$ $(n-12)(n+9)=0$ $\Rightarrow$ $n=12$ $(\because n\ne -9)$