A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

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Oddman Profile
Oddman answered
You can write a quadratic equation, or you can estimate, or you can make an educated guess.
  108 = 1*108 = 2*54 = 3*36 = 4*27 = 6*18 = 9*12
The dimensions 9 by 12 are each 3 ft less than the dimensions 12 by 15. The border will be half of 3 ft, that is 1.5 ft.
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The perimeter of the room is 2(12+15)=54 ft. The difference between the area of the room and the area of the rug is 180 ft^2 - 108 ft^2 = 72 ft^2, so the width of the border can be estimated as slightly more than 72ft^2/(54ft), about 1.5 ft.

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