Question

if $overline{fi}congoverline{hi}$, $fg = w + 18$, and $gh = 2w$, what is the value of $w$?

Explanation:

Step1: Apply property of congruent segments

Since $\overline{FI}\cong\overline{HI}$, point $I$ lies on the perpendicular - bisector of $\overline{FH}$. And by the property of the perpendicular - bisector, $FG = GH$.
$w + 18=2w$

Step2: Solve the equation for $w$

Subtract $w$ from both sides of the equation.
$18=2w - w$
$w = 18$

Answer:

$18$