Stuck on Square Root Problem (yep, homework!) Here's the simple question: Devon has a piece of poster board 45 cm by 20 cm. His teacher challenges him to cut the board into parts, then rearrange the parts to form a square. a) What is the side length of the square? b) What are the fewest cuts Devon could have made? Explain. I understand part a (the answer is 30 or the square root of 900) but how many cuts would he have made to make it a square? 45+20 = 65, 65 doesn't divide in 30 and if I try taking 45-15 and moving the 15 to the 20, I now get 35*30 which is not = 900 (1050)? How come then, 45*20 = 90 but when you displace 15, you get a greater answer? I'm sure the error is somewhere in my conversion between the rectangle and the square.

The issue with your calculations is that when you cut the 45 off at the 30/15 mark, you get a piece that is 20*30 and a piece that is 20*15. Putting the 20*15 piece along the 20*30 piece will give you an L-shape, that is 35*30 with a 10*15 rectangle cut out of the corner.

The best way that I can see to do this is in two cuts. First, make the cut that you describe. Now, you have a 20*30 piece and a 20*15 piece. Cut the 20*15 piece into two 10*15 pieces. Now, put those two pieces together along their 10 edges, giving a 10*30 piece. Now, put the 10*30 next to the 20*30 piece along 30 edges, giving a 30*30 square in two cuts.