Question

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in △ abc, ge = 27 in.
what is the length of \\(\overline{be}\\)?
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\\(\square\\) in.

Explanation:

Step1: Identify Centroid Property

In a triangle, the centroid (G) divides each median into a ratio of 2:1, with the longer segment being closer to the vertex. So, \( BG:GE = 2:1 \), meaning \( BE=BG + GE \) and \( BG = 2 \times GE \).

Step2: Calculate BG Length

Given \( GE = 27 \) in, \( BG = 2\times27 = 54 \) in.

Step3: Calculate BE Length

\( BE=BG + GE = 54 + 27 = 81 \) in.

Answer:

81