An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $$\frac{N}{20}ma^2$$ where N is an integer. The value of N is __________.

Perpendicular distance of mass at E from axis EX: $$r_E = 0$$

Perpendicular distance of mass at G from axis EX: $$r_G = a$$

Perpendicular distance of mass at F from axis EX: $$r_F = a \cos(60^\circ) = \frac{a}{2}$$

Total moment of inertia of the system about axis EX: $$I = m r_E^2 + m r_G^2 + m r_F^2$$

$$I = m(0)^2 + m(a)^2 + m\left(\frac{a}{2}\right)^2 = ma^2 + \frac{ma^2}{4} = \frac{5}{4}ma^2$$

$$I = \frac{5 \times 5}{4 \times 5}ma^2 = \frac{25}{20}ma^2$$

$$\frac{N}{20}ma^2 = \frac{25}{20}ma^2 \implies N = 25$$