point g is the centroid of triangle abc. ag = (5x + 4) units and gf = (3x - 1) units. what is af? 11 units…

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

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

Answer:

D. 51 units

Explanation:

Step1: Recall centroid property

The centroid divides each median in a 2:1 ratio. So, $AG = 2GF$.

Step2: Set up equation

$5x + 4=2(3x - 1)$.

Step3: Expand right - hand side

$5x + 4 = 6x-2$.

Step4: Solve for x

$4 + 2=6x - 5x$, so $x = 6$.

Step5: Find GF

Substitute $x = 6$ into $GF=3x - 1$, then $GF=3\times6 - 1=17$ units.

Step6: Find AF

Since $AF=AG + GF$ and $AG = 2GF$, then $AF=3GF$. Substitute $GF = 17$ into it, $AF = 3\times17=51$ units.