cut a square out of a rectangle (2011 All-Ukrainian Correspondence MO 5-12 p3)
Source:
April 29, 2021
geometryrectanglesquareUkraine Correspondence
Problem Statement
The kid cut out of grid paper with the side of the cell rectangle along the grid lines and calculated its area and perimeter. Carlson snatched his scissors and cut out of this rectangle along the lines of the grid a square adjacent to the boundary of the rectangle.
- My rectangle ... - kid sobbed. - There is something strange about this figure!
- Nonsense, do not mention it - Carlson said - waving his hand carelessly. - Here you see, in this figure the perimeter is the same as the area of the rectangle was, and the area is the same as was the perimeter!
What size square did Carlson cut out?