Questions: If GF=71, calculate JG. JG=

If GF=71, calculate JG. JG=
Transcript text: If $G F=71$, calculate $J G$. \[ J G= \]
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Solution

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Solution Steps

Step 1: Determine the relationship between GF and JG.

G is the centroid of triangle DEF. The medians intersect at G. Each median is divided into two segments at the centroid, with the segment from the centroid to the vertex being twice the length of the segment from the centroid to the midpoint of the opposite side. Therefore, GF is twice the length of JG.

Step 2: Set up an equation.

Since GF is twice the length of JG, the equation is GF = 2 * JG.

Step 3: Solve the equation for JG.

Given that GF = 71, substitute this value into the equation: 71 = 2 * JG. Divide both sides of the equation by 2: JG = 71 / 2 JG = 35.5

Final Answer: The length of JG is 35.5.

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