Fáry [3] proved that all planar graphs can be drawn in the plane using only straight line segments. Harborth et al. [7] ask whether or not there exists such a drawing where all edges have integer lengths, and Geelen et al. [4] proved that cubic planar graphs satisfied this conjecture. We re-prove their result using rigidity theory, exhibit other natural families of planar graphs that satisfy this conjecture as immediate corollaries, and also prove a weaker result for all planar graphs in R 3. 