6.1. A rectangle with a perimeter of 100 cm was divided into 88 smaller identical rectangles by seven vertical and ten horizontal cuts. What is the perimeter of each of them, if the total length of all the cuts is 434 cm?

## Answer: 11
Solution. Note that the sum of seven vertical and seven horizontal cuts is 7.50 $=350$ cm, so the three extra horizontal cuts have a total length of 84 cm, each of which is 28 cm. This is the length of the horizontal side of the original rectangle. The vertical side of it is $50-28=22$ cm. After the cuts, the resulting rectangle has a horizontal side of $28 / 8=3.5$ cm and a vertical side of $22 / 11=2$ cm, so its perimeter is 11 cm.