## Task 1 - 050521

From 36 equally large squares, a rectangle is to be formed by placing them together.

a) How many solution possibilities are there? (In each solution, all squares should be used.)

b) Which of the possible rectangles has the smallest perimeter?
a) The area of the rectangle is 36 square units. The length of each rectangle side must, due to the construction, be an integer multiple of the length of a square side. Therefore, there are the following 5 possibilities:

1. Rectangle: Length 1, Width 36, Perimeter 74 units,
2. Rectangle: Length 2, Width 18, Perimeter 40 units,
3. Rectangle: Length 5, Width 12, Perimeter 30 units,
4. Rectangle: Length 4, Width 9, Perimeter 26 units,
5. Rectangle: Length 6, Width 6, Perimeter 24 units.

b) Among these rectangles, the 5th rectangle (square) has the smallest perimeter.