8. Find x and then measure of each side of the triangle.

Question

Triangle FGH is equilateral with FG= x+5, GH=3x-9, and FH=2x-2

Answer 1

FG = x+5

GH = 3x-9

FH = 2x-2

 

Because the triangle is equilateral, all sides are the same length.  Thus we can set any two sides equal and solve for x:

 

FG = GH

x + 5 = 3x - 9

14 = 2x

 

7 = x

 

The lengths of the sides are:

FG = x+5 = 7+5 = 12
GH = 3x-9 = 3*7 - 9 = 21-9 = 12

FH = 2x-2 = 2*7 -2 = 14-2 = 12

 

FG = GH = FH = 12