Questions: Each figure shows a triangle with one or more of its medians. Find x if RE=x-1 and GE=2x-12

Each figure shows a triangle with one or more of its medians. Find x if RE=x-1 and GE=2x-12
Transcript text: Each figure shows a triangle with one or more of its medians. 2) Find $x$ if $R E=x-1$ and $G E=2 x-12$
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Solution

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Solution Steps

Step 1: Set up the equation

RE is a median of triangle QRP, and G is the centroid. The centroid divides the median into segments in a 2:1 ratio, with GE being the shorter segment and RG being the longer segment. Therefore, RE = RG + GE, and RG = 2 * GE. We can write RE = 3 * GE or GE = RE / 3.

Step 2: Solve for x

Given RE = x - 1 and GE = 2x - 12, we have: 2x - 12 = (x-1)/3 Multiplying both sides by 3: 6x - 36 = x - 1 5x = 35 x = 7

Final Answer

x = 7

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