Problem 4.6.2 A rectangle with a perimeter of 100 cm is divided into 70 identical smaller rectangles by six vertical and nine horizontal cuts. What is the perimeter of each of them, if the total length of all the cuts is 405 cm $?$
# Answer: 13

Solution. Note that the sum of six vertical and six horizontal cuts is $6 \square 50=300$ cm, so the three extra horizontal cuts have a total length of 105 cm, each being 35 cm. This is the length of the horizontal side of the original rectangle. The vertical side of the rectangle is $50-35=15$ cm. After the cuts, the resulting rectangle has a horizontal side of $35 / 7=5$ cm and a vertical side of $15 / 10=1.5$ cm, so its perimeter is 13 cm.