A city consists of 5 identical squares arranged in such a way that the city's layout forms a cross with equal arms. The stone wall surrounding the city is as many kilometers long as the city's area in square kilometers. How long is the stone wall?

The city's area is made up of 5 identical squares arranged to form a cross. The stone wall surrounding the city is as many kilometers long as the city's area in square kilometers. What is the length of the stone wall?
Let's denote the side of the congruent squares as $a$.

![](https://cdn.mathpix.com/cropped/2024_05_02_f5fff2842b676fd7f3c5g-1.jpg?height=309&width=371&top_left_y=225&top_left_x=866)

The perimeter of the city is then $12a$, and its area is $5a^2$. The two quantities are numerically equal:

$$
5a^2 = 12a
$$

Dividing both sides by $a \neq 0$ and rearranging:

$$
a = \frac{12}{5} = 2.4
$$

The length of the wall is $12a = 28.8 \text{ km}$.

Tamás Hornyánszky (Bp. VIII., Piarist g. II. o. t.)