Problem 4. A random point inside a square is equally distant from the two opposite sides, and those distances are $3 x+1$ and $5 x-7$ respectively, measured in cm. Determine the perimeter of the square.
Solution. From the condition of the problem, we have $5 x-7=3 x+1$, from which $x=$ 4. The side of the square is $5 x-7+3 x+1=26 \mathrm{~cm}$, and the perimeter is $4 \cdot 26=104 \mathrm{~cm}$.

## VI section