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Point G is the centroid of triangle abc use the information to find the value of x.

1. GC=3x +7 and CE= 6x

2. FG= x +8 and AF = 9x - 6

3. Bg=5x -1 and DG = 4x -5

User Nabinca
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2 Answers

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2. FG= x +8 and AF = 9x - 6
User RezKesh
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The value of x is 7/6.

To find the value of x, we can utilize the given information about the lengths of the medians and segments within triangle ABC.

Using medians CE and GC:

Since G is the centroid of triangle ABC, it divides each median into two segments in a ratio of 2:1. Therefore, we can set up two equations based on the given lengths:

CE = 2/3 * GC

6x = 2/3 * (3x + 7)

Solving for x, we get:

6x = 2x + 14/3

4x = 14/3

x = 7/6

Using medians BG and FG:

Similarly, we can set up two equations based on the given lengths of medians BG and FG:

FG = 2/3 * BG

x + 8 = 2/3 * (5x - 1)

Solving for x, we get:

x + 8 = 10x/3 - 2/3

8/3 = 9x/3

x = 8/9

Using medians DG and AG:

Following the same approach, we can set up two equations based on the given lengths of medians DG and AG:

AG = 2/3 * DG

9x - 6 = 2/3 * (4x - 5)

Solving for x, we get:

9x - 6 = 8x/3 - 10/3

x - 6 = 8x/3 - 10/3

-5 = 5x/3

x = -3

Comparing the values obtained from each set of equations, we find that x = 7/6 is consistent across all three sets. Therefore, the value of x is 7/6.

User Geedubb
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