Question

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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Answer 1

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∆ GHJ is an Equilateral triangle ,

Thus the sides are same.

So :

GH = HJ = GJ

`2x + 17 = 6x - 19 = 4x - 1`

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`2x + 17 = 6x - 19`

Add sides 19

`2x + 17 + 19 = 6x - 19 + 19 \\`

`2x + 36 = 6x`

Subtract sides 2x

`- 2x + 2x + 36 = - 2x + 6x`

`36 = 4x`

`4x = 36`

Divide sides by 4

`(4x)/(4) = (36)/(4) \\`

`x = 9`

So ;

`GH = 2(9) + 17`

`GH = 18 + 17`

`GH = 35`

Thus ;

`GH = HJ = GJ = 35`

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