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

Explanation:

Step1: Apply centroid ratio property

The centroid divides a median into a 2:1 ratio, so $AG = 2 \times GF$.
$5x + 4 = 2(3x - 1)$

Step2: Solve for x

Expand and simplify the equation:
$5x + 4 = 6x - 2$
$4 + 2 = 6x - 5x$
$x = 6$

Step3: Calculate AG and GF

Substitute $x=6$ into the expressions:
$AG = 5(6) + 4 = 34$
$GF = 3(6) - 1 = 17$

Step4: Find length of AF

AF is the sum of AG and GF:
$AF = AG + GF$
$AF = 34 + 17$

Answer:

43 units