With a compass and straightedge, is it possible to construct the square of a given distance?

Question

Given two line segments A and B of arbitrary length, is it possible to construct a segment C such that the proportion of C to A is equal to the proportion of [the area of a square with side B] to [the area of a square with side A]?

Answer 1

Hint If $DEF$ is a right triangle, $D=90^\circ$ and $DH$ is the altitude, then $$DH^2=EH \cdot FH$$ Now construct a right triangle such that $EH=1$ and $DH$ is the given distance.