Question

what is the value of k?
gh is the perpendicular bisector of ef where ef = 2k + 11, gf = 5k + 28, and ge = 8k + 4

Explanation:

Step1: Use property of perpendicular bisector

Since $\overline{GH}$ is the perpendicular bisector of $\overline{EF}$, we know that $GF = GE$.
So, $5k + 28=8k + 4$.

Step2: Solve the equation for k

Subtract $5k$ from both sides: $28 = 3k+4$.
Then subtract 4 from both sides: $24 = 3k$.
Divide both sides by 3: $k = 8$.

Answer:

$8$