by Dave Youngs
Squarely Constructed I is a modification of a puzzle brought to my attention by an AIMS colleague, Richard Thiessen. When Richard presents this puzzle, he hands out a paper rectangle that is nine inches long and four inches wide. His challenge is to cut the rectangle into two pieces that can be rearranged into a square. In Squarely Constructed I, students are given 9 X 4 rectangular grids that can be cut out and used to solve the problem. With a bit of mathematical thinking, students should discover that the area of the rectangular grid is 36 square units, thus the two pieces formed by cutting the rectangle apart should produce a 6 X 6 square. Armed with this knowledge, students should be able to work out a solution.
This version of the puzzle is the simpler of two versions. We hope that you enjoy this puzzle. Check back next month for a more challenging version of this puzzle!