Question

1. FGH Is equilateral. FG = x+5,GH = 3x - 9 and FH - 2x - 2.Find x and the measure of each side.FGGH =FH =

Answer 1

since FGH is an equilateral triangle, all its sides are equal, therefore

`FG=GH=FH`

then

`\begin{gathered} x+5=3x-9 \\ x+5-5=3x-9-5 \\ x=3x-14 \\ x-3x=3x-14-3x \\ -2x=-14 \\ -(2x)/(-2)=-(14)/(-2) \\ x=7 \end{gathered}`

answer: x = 7

for FG:

`FG=x+5=7+5=12`

answer: FG = 12

for GH:

`GH=3x-9=3(7)-9=21-9=12`

answer: GH = 12

for FH:

`FH=2x-2=2(7)-2=14-2=12`

answer: FH = 12