Find the value of x for which the triangle with vertices (2, 2), (4, 5) and (x, 8) will have the centroid (0, 5).

We know, the centroid of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) = $\left(\frac{{\mathrm{x}}_1 + {\mathrm{x}}_2 + {\mathrm{x}}_3}{3} , \frac{{\mathrm{y}}_1 + {\mathrm{y}}_2 + {\mathrm{y}}_3}{3} \right)$

Given vertices of the triangle = (2, 2), (4, 5), and (x, 8) 

Given centroid = (0, 5)

Thus, 

$(\frac{2+4+\mathrm{x}}{3},\frac{2+5+8}{3})=(0, 5)$

Comparing the x coordinates, we get:

$\Rightarrow \frac{2+4+\mathrm{x}}{3}=0$

$\Rightarrow \frac{6+\mathrm{x}}{3}=0$

$\Rightarrow \text{x = -6}$