help with math question

Question

Find x and the measure of each side of ??GHJ if the triangle is isosceles with HG=JG, GH = x+7, GJ =3x-5 and HJ =x-1

Answer 1

Hi Kiki, the length of the sides of an isosceles triangle are equal, then GH must equal GJ.

 

Equate GH to GJ to find x:

 

x + 7 = 3x - 5

 

Add 5 to both sides:

 

x + 12 = 3x

 

Subtract x from both sides:

 

2x = 12

 

Divide both sides by 2:

 

x = 6

 

Then leg GH = 6 + 7, or 13

 

Leg GJ = 3x - 5, or 3 * 6 - 5 = 13

 

Finally, leg HJ = x - 1, or 5

 

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