A polygon has 54 diagonals. Then, the number of its sides is

Step-by-step solution

Number of diagonals in polygon =54 Let the number of sides in polygon =n Then, The number of diagonal in any polygon = n(n-3) 2 54= n(n-3) 2 n^2-3 n=108n^2-3 n-108=0n^2-12 n+9 n-108=0n(n-12)+9(n-12)=0(n+9)(n-12)=0n=-9 or n=12 (not possible) Hence, the number of sides in polygon is n=12