2 [Rectangles and Squares. Properties and Characteristics]

Auto: Dorricheno $C$.

Which are more numerous: rectangles with integer sides and a perimeter of 1996, or rectangles with integer sides and a perimeter of 1998?

(Rectangles $a \times b$ and $b \times a$ are considered the same.)
If the perimeter of a rectangle is 1996, then the sum of the lengths of its adjacent sides is 998.

## Solution

If the perimeter of a rectangle is 1996, then the sum of the lengths of its adjacent sides is 998. This means the length of the shorter side can take values from 1 to 499. If the perimeter of the rectangle is 1998, then the sum of the lengths of its adjacent sides is 999, and the length of the shorter side can take the same values: from 1 to 499. Thus, in both cases, there are the same number of rectangles, which is 499.

## Answer

The same number.