Given information:
- Two sides of the triangle are 2x + y = 0 and x - y + 2 = 0.
- The orthocentre of the triangle is (2, 3).

Step 1: Find the slopes of the given lines
To find the slopes of the given lines, we need to put them in the slope-intercept form (y = mx + c), where m is the slope.

The first line, 2x + y = 0, can be rewritten as y = -2x.

The slope of this line is -2.

The second line, x - y + 2 = 0, can be rewritten as y = x + 2.

The slope of this line is 1.

Step 2: Find the slopes of the lines perpendicular to the given lines
To find the slopes of the lines perpendicular to the given lines, we need to take the negative reciprocal of the slopes of the given lines.

The negative reciprocal of -2 is 1/2.

The negative reciprocal of 1 is -1.

Step 3: Find the equations of the altitudes passing through the orthocentre
Since the orthocentre is the point of intersection of the altitudes of a triangle, we can find the equations of the altitudes passing through the orthocentre using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) is the orthocentre and m is the slope of the altitude.

For the first altitude, with slope 1/2 passing through (2, 3), the equation can be written as y - 3 = 1/2(x - 2), which simplifies to y = (1/2)x + 2.

For the second altitude, with slope -1 passing through (2, 3), the equation can be written as y - 3 = -1(x - 2), which simplifies to y = -x + 5.

Step 4: Find the intersection point of the altitudes
To find the intersection point of the altitudes, we need to solve the system of equations formed by the equations of the altitudes.

Substituting y = (1/2)x + 2 into y = -x + 5, we get (1/2)x + 2 = -x + 5.

Simplifying the equation, we get (5/2)x = 3, which gives us x = 6/5.

Substituting this value of x back into y = (1/2)x + 2, we get y = (1/2)(6/5) + 2, which simplifies to y = 17/5.

Therefore, the intersection point of the altitudes is (6/5, 17/5).

Step 5: Find the third side of the triangle
The third side of the triangle can be found by finding the distance between the intersection point of the altitudes and any of the given points.

Let's find the distance between (6/5, 17/5) and the point (0, 0) using the distance formula.

The distance formula is given by: distance = sqrt((x2 - x1)^2 +