Solution:
we are given that
If G is the midpoint of FH, it mean that
[tex]FG=GH[/tex]
we are also given that
[tex]FG=11x-7 ,GH= 3x+9[/tex]
So we can write
[tex]11x-7=3x+9\\ \\ 11x-3x=7+9\\ \\ 8x=16\\ \\ x=2[/tex]
So [tex]FG=11x-7=11*\frac{1}{2}-7=11*2-7=15[/tex]
Using the midpoint concept, it is found that: FG = 15.
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G is the midpoint of FH, and thus:
[tex]FG = GH[/tex]
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We are given:
Using this, we find x.
[tex]FG = GH[/tex]
[tex]11x - 7 = 3x + 9[/tex]
[tex]11x - 3x = 9 + 7[/tex]
[tex]8x = 16[/tex]
[tex]x = \frac{16}{8}[/tex]
[tex]x = 2[/tex]
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Having x, we can find FG.
[tex]FG = 11x - 7 = 11(2) - 7 = 22 - 7 = 15[/tex]
Thus, FG = 15.
A similar problem is given at https://brainly.com/question/10956693
