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if GHJ is an equilateral triangle, GH = 2x +17, HJ = 6x-19, and GJ = 4x-1, find X and the measure of each side..


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∆ GHJ is an Equilateral triangle ,

Thus the sides are same.

So :

GH = HJ = GJ

[tex]2x + 17 = 6x - 19 = 4x - 1[/tex]

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[tex]2x + 17 = 6x - 19[/tex]

Add sides 19

[tex]2x + 17 + 19 = 6x - 19 + 19 \\ [/tex]

[tex]2x + 36 = 6x[/tex]

Subtract sides 2x

[tex] - 2x + 2x + 36 = - 2x + 6x[/tex]

[tex]36 = 4x[/tex]

[tex]4x = 36[/tex]

Divide sides by 4

[tex] \frac{4x}{4} = \frac{36}{4} \\ [/tex]

[tex]x = 9[/tex]

So ;

[tex]GH = 2(9) + 17[/tex]

[tex]GH = 18 + 17[/tex]

[tex]GH = 35[/tex]

Thus ;

[tex]GH = HJ = GJ = 35[/tex]

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