Question

if cf = ef = 30, cd = b + 22, and de = 2b, what is the value of b?

Explanation:

Step1: Apply property of perpendicular bisector

Since $CF = EF$ and $DF$ is perpendicular to $CE$, then $CD=DE$ (a point on the perpendicular - bisector of a line segment is equidistant from the endpoints of the line segment).
$b + 22=2b$

Step2: Solve the equation for $b$

Subtract $b$ from both sides of the equation $b + 22=2b$.
$22=2b - b$
$b = 22$

Answer:

$22$