Turning a rectangle into a square by dissection
Consider a rectangle with sides a and b, such that, a < b < 2*a. We show here one way to cut it into three pieces and rearrange them into a square.
Compute, s = √(a*b). Open a compass to length s, put a pin in corner A of the rectangle, and mark point X on side CD. The distance AX is s. Draw the line AX. Draw another line (using an index card) BY, perpendicular to AX.
Cut out the rectangle ABDC, cut the line AX, and cut the line YB.
In order to get a square in slanted position, move the left triangle to the right, and move the top triangle to the bottom right.
Remark.
Notice that the length BY is also s. (Why?)
Task.
Convert a rectangle 2 inches by 3 inches into a square.