2007 AMC 10B Problem 10

Taking $BC$ as the base, the area is $\dfrac12(BC)d,$ where $d$ is the distance from $A$ to line $BC.$ The area equals $1$ exactly when $d=\dfrac{2}{BC}.$ The points at this fixed distance from line $BC$ form two lines parallel to $BC,$ one on each side. Thus, the correct answer is A.