Question

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units. What is AF? 11 units 15 units 43 units 51 units

Answer 1

see the attached figure to better understand the problem

we know that

The point G is where all medians intersect and is often described as the triangle's center of gravity or centroid. It is formed by the intersection of the medians. The centroid divides each median in a ratio of $\frac{2}{1}$

so

$\frac{AG}{GF} =\frac{2}{1} \\\\ \frac{5x+4}{3x-1}=\frac{2}{1}\\ \\ (3x-1)*2=5x+4\\ \\ 6x-2=5x+4 \\\\ 6x-5x= 4+2\\\\ x=6\ units$

Find the value of FA

$FA=(5x+4)+(3x-1)\\ \\FA=8x+3\\ \\FA=8*6+3\\ \\FA=51 units$

therefore

the answer is

$51 units$

Answer 2

the answer is 51 units