The length of a rectangle piece of paper is 20 cm and the breadth is 10 cm. if this paper has to be separated into square shaped pieces, without any waste, draw the ways how that separation could be done and write the length of one side of each square piece. find the area of each of the separated pieces

The best way ( meaning, the way that results squares with the biggest areas ) is to cut it in 2 squares with the lenght of 10cm. Then, the area is 10*10 cm = 100 cm^2

Why cut it like this? We find the highest number that divides both 20 and 10, in this case it's 10. Then, we can cut squares with the lenght of 10 cm. But we have a rectangle with the area of 20*10=200 cm^2 , and we cut squares of 10*10=100cm^2. 200/100=2. So we cut 2 squares Also, you could say that it's because the simmetry line cuts the rectangle in 2 other simetrical rectangles, which in this case, happen to be squares.