Consider a polygon of ‘n’ sides. If the number of diagonal of polygon is 65 then how many triangles can be drawn from taking vertices of polygon as vertices of triangle

(Q). Consider a polygon of ‘n’ sides. If the number of diagonal of polygon is 65 then how many triangles can be drawn from taking vertices of polygon as vertices of triangle?
Solution:-
number of diagonal of polygon = 65
∴ ⁿC₂ – n = 65
     = 65
n(n-3) = 2×5×13

∴ n = 13

So polygon has 13 vertices
now taking theser vertices as vertices of a traingle, number of triangle = ¹³C₃
= 286         Answer