Step the Square
The solution to this puzzle is shown in the illustration.
The solution is based on a dissection that uses the step
technique, so named because of the resemblance to stair steps. Girolamo Cardano, an
Italian physician and mathematician, described this dissection in 1663 in
his De Rerum Varietate.
Greg N. Frederickson in his Dissections: Plane & Fancy writes:
"...In its simplest form, the step technique cuts a rectangle in a zigzag
pattern, alternating horizontal cuts of one length with vertical cuts of
another. By shifting the two resulting pieces by one step relative to each
other, we form a different rectangle..."
For more information on dissections including this one see Dissections:
Plane & Fancy by Greg N. Frederickson.