Question

Point G is between points F and H. FH = 102, FG = 5x + 9, and HG = 9x − 5. Show your work.

A.) What is the value of x ?
B.) What is the length of ̅̅̅̅FG?
C.) What is HG?

Answer 1

Refer to the diagram shown below.

FH = FG + GH, therefore
(5x + 9) + (9x - 5) = 102
5x + 9 + 9x - 5 = 102
14x + 4 = 102
Subtract 4 from each side.
14x = 98
Divide each side by 14.
x = 7

FG = 5x + 9 = 5*7 + 9 = 35 + 9 = 44
HG = 9x - 5 = 9*7 - 5 = 63 - 5 = 58

Answers:
Part A) x = 7
Part B) FG = 44
Part C) HG = 58