The measure of AM is 12
Here, we are to find the measure of AM
Mathematically, the centroid divides the median on which it lies into 2 parts
These parts are usually in the ratio 1 to 2
What this mean is that if we multiply the smaller side by 2, we get the larger side
That would proceed as follows;
[tex]\begin{gathered} 2(2x-4)\text{ = x + 4} \\ 4x\text{ - 8 = x + 4} \\ \\ 4x-x\text{ = 8 + 4} \\ \\ 3x\text{ = 12} \\ \\ x\text{ = }\frac{12}{3} \\ \\ x\text{ = 4} \end{gathered}[/tex]
Now, the length of the median is the sum of the two parts
Mathematically, that would be;
[tex]\begin{gathered} AM\text{ = x + 4 + 2x-4} \\ \\ AM\text{ = 3x} \\ \\ \text{Substituting x =4} \\ \\ AM\text{ = 3(4) = 12} \end{gathered}[/tex]
