Question

if gj = ij = 42, gh = v + 40, and hi = 6v, what is the value of v?

Explanation:

Step1: Use property of perpendicular bisector

Since $GJ = IJ$ and $J$ lies on the perpendicular - bisector of $GI$, then $GH=HI$ (a point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment).
$v + 40=6v$

Step2: Solve the equation for $v$

Subtract $v$ from both sides of the equation:
$40 = 6v - v$
$40=5v$
Then divide both sides by 5:
$v=\frac{40}{5}$

Answer:

$8$