# A rectangle in a rectangular hole

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)

• 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.
– smci
Apr 20, 2020 at 6:46
• I think a room of size 72 would be slightly less plausible, be that in ft^2, yd^2 or m^2. Apr 21, 2020 at 15:05
• @subdermatogylphic: I said scaled down; note that's why the resulting measurements (12x6 or 9x8) are unitless. They have no units.
– smci
Apr 22, 2020 at 5:58
• @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. Apr 22, 2020 at 6:33
• @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...
– smci
Apr 22, 2020 at 6:42