What are our Givens?
m = 26-kg
H = 2.5-m
W = 0.80-m
d = 0.20-m = distance of a hinge from its closest edge
What's it asking?
What is the horizontal force the two hinges exert.
H_t = ? (top hinge horizontal force)
H_b = ? (bottom hinge horizontal force)
Use the fact the Net Torque = 0 and one of the hinges as a reference point to find the Horizontal force of one of the hinges.
We're going to use the bottom hinge as the reference point.
Tq = H_t * (H - 2d) - m * g * W / 2 = 0
H_t = m * g * W / 2 * / (H-2d)
Plug in the variables to solve for H_t
H_t = 26-kg * 9.81-m/s^2 * 0.8-m / 2 / (2.5-m - 2*0.2-m)
H_t = 48.59-kg*m/s^2 = 48.59-N
Because the directions specified that the force going towards the hinges (to the left) is negative, H_t is a negative value.
H_t = -48.95-N
Now we have to find H_b.
Because the system is in static equilibrium and we know one of the two forces acting in the y direction, expressing the forces in the y direction will enable us to solve for H_b.
Fy = H_t + H_b = 0
>> H_b = -H_t
H_b = 48.95-N