Question

given △abc with medians \\(\overline{al}\\), \\(\overline{bf}\\), and \\(\overline{ce}\\) intersecting at centroid g.
if \\(cg = (7x - 13)\\) m, and \\(ge = 25\\) m, determine the value of \\(x\\).
\\(x = \square\\)

Explanation:

Step1: Recall centroid property

The centroid divides each median in a ratio of \(2:1\). So \(CG = 2\times GE\).

Step2: Substitute values

Given \(CG=(7x - 13)\text{ m}\) and \(GE = 25\text{ m}\). Then \(7x-13=2\times25\).

Step3: Solve the equation

$$
LATEXBLOCK0
$$

Answer:

\(9\)