Question

given △abc with medians \\(\overline{al}\\), \\(\overline{bf}\\), and \\(\overline{ce}\\) intersecting at centroid g. if cg = (5x + 43) m, and ge = 34 m, determine the value of x. x = \square

Explanation:

Step1: Recall centroid property

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

Step2: Substitute the given values

Given \( CG=(5x + 43)\text{ m}\) and \( GE = 34\text{ m}\). Substitute into \( CG = 2\times GE\):
\(5x+43=2\times34\)

Step3: Simplify the right - hand side

\(2\times34 = 68\), so the equation becomes \(5x+43 = 68\).

Step4: Solve for \(x\)

Subtract 43 from both sides: \(5x=68 - 43\).
\(5x=25\).
Divide both sides by 5: \(x=\frac{25}{5}\).

Answer:

\(x = 5\)