I have a carpet of 240 inches by 120 inches, but my floor, which it needs to cover, is 180 inches by 160 inches. How can I do this by cutting the carpet into exactly two pieces?

Source: Rational Amusement for Winter Evenings by John Jackson (Google Books link)

  • $\begingroup$ In simplest terms, scaling down by the common denominator of 20 (inches), the carpet is 12 x 6, and the hole is 9 x 8. Both have area 72. $\endgroup$
    – smci
    Apr 20, 2020 at 6:46
  • $\begingroup$ I think a room of size 72 would be slightly less plausible, be that in ft^2, yd^2 or m^2. $\endgroup$ Apr 21, 2020 at 15:05
  • $\begingroup$ @subdermatogylphic: I said scaled down; note that's why the resulting measurements (12x6 or 9x8) are unitless. They have no units. $\endgroup$
    – smci
    Apr 22, 2020 at 5:58
  • $\begingroup$ @smci I know scaling down could be useful, but I meant that the exact numbers and units given are the most viable for posing a realistic question involving a carpet and a room without any need for me to edit the original puzzle much. $\endgroup$ Apr 22, 2020 at 6:33
  • $\begingroup$ @subdermatogylphic: ok. Btw if you think 9 x 8 ft room is outlandish, see the trends towards 'tiny houses', 'microapartments' and adult dormitories in superheated property markets like SF... $\endgroup$
    – smci
    Apr 22, 2020 at 6:42

2 Answers 2


The scale is not consistent on the drawing:



In addition to trolley813's two step cut, you can do a three-step cut to produce the same results rotated 90 degrees. Not precisely to scale: enter image description here


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