Final answer:
To find the length of GH, set the expressions for GF and FH equal to each other and solve for x. Substitute the value of x into either GF or FH to find the length of GH.
Step-by-step explanation:
To find the length of GH, we need to first find the value of x. Since f is the midpoint of GH, GF is equal to FH.
Setting the two expressions for GF and FH equal to each other and solving for x, we get:
10x + 2 = 6x + 22
Subtracting 6x from both sides and subtracting 2 from both sides, we get:
4x = 20
Dividing both sides by 4, we get:
x = 5
Now that we have the value of x, we can substitute it into either GF or FH to find the length of GH. Let's substitute it into GF:
GF = 10(5) + 2
GF = 52
Therefore, the length of GH is 52 units.