Question 46
Let $ABCD$ be a rectangle with $AB = 3$ and $BC = 7$. Let $W$ be a point on segment $AB$ such that $AW = 1$. Let $X, Y, Z$ be points on segments $BC, CD, DA$, respectively, so that quadrilateral $WXYZ$ is a rectangle, and $BX \lt XC$. Determine the length of segment $BX$.