Problem 4.6.3 A rectangle with a perimeter of 96 cm was divided into 108 smaller identical rectangles by eight vertical and eleven horizontal cuts. What is the perimeter of each of them, if the total length of all the cuts is 438 cm?
# Answer: 9

Solution. Note that the sum of eight vertical and eight horizontal cuts is $8 \square 48=384$ cm, so the three extra horizontal cuts have a total length of 54 cm, each of which is 18. This is the length of the horizontal side of the original rectangle. The vertical side of it is $48-18=30 \text{~cm}$. After the cuts, the resulting rectangle has a horizontal side of $18 / 9=2$ cm, and a vertical side of $30 / 12=2.5$ cm, so its perimeter is 9 cm.