[tex]PC\text{ = 2(3x-3) = 36}[/tex]
Here, we want to find the length of PC
As we can see from the figure provided, the point P represents the centroid of the triangle
The centroid divides each median length into lengths of ratio 2 to 1
SC is divided into 2 parts; SP and PC; with the length of PC twice that of SP
The addition of the two will give SC
Thus, we have it that;
[tex]\begin{gathered} 3x-3\text{ + 2(3x-3) = 7x + 5} \\ 3x-3+6x-6\text{ = 7x + 5} \\ 3x+6x-3-6\text{ = 7x + 5} \\ 9x-9\text{ = 7x+5} \\ 9x-7x\text{ = 5+9} \\ 2x\text{ = 14} \\ x\text{ = }\frac{14}{2} \\ x\text{ = 7} \end{gathered}[/tex][tex]\begin{gathered} PC\text{ = 2(3x-3)} \\ PC\text{ = 2(3(7)-3)} \\ PC\text{ = 2(21-3)} \\ PC\text{ = 2(18)} \\ PC\text{ = 36} \end{gathered}[/tex]
