Problem 8.1. A square was cut into four equal rectangles, and from them, a large letter P was formed, as shown in the figure, with a perimeter of 56.
![](https://cdn.mathpix.com/cropped/2024_05_06_a7569897979ba1659de3g-27.jpg?height=356&width=720&top_left_y=274&top_left_x=366)

What is the perimeter of the original square
Answer: 32.

Solution. Let the width of the rectangle be $x$. From the first drawing, we understand that the length of the rectangle is four times its width, that is, it is equal to $4 x$. Now we can calculate the dimensions of the letter P.

![](https://cdn.mathpix.com/cropped/2024_05_06_a7569897979ba1659de3g-27.jpg?height=381&width=289&top_left_y=940&top_left_x=582)

From this, we get the equation

$$
\begin{gathered}
28 x=56 \\
x=2
\end{gathered}
$$

The perimeter of the square is $16 x=32$.