[ Properties and characteristics of a parallelogram ]

The diagonals of parallelogram $A B C D$ intersect at point $O$. The perimeter of the parallelogram is 12, and the difference in the perimeters of triangles $B O C$ and $C O D$ is 2. Find the sides of the parallelogram.
Compose a system of equations with respect to the unknown sides of the parallelogram.

## Solution

Let $A B=C D=a, B C=A D=b$. According to the problem,

$$
12=2 a+2 b \text{ and } 2=(b+O B+O C)-(a+O D+O C)=b-a,
$$

From the obtained system of equations, we find that $a=2, b=4$.

## Answer

$2,4,2,4$.