SOLUTION: Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 300 square feet of

Question 1066600: Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 300 square feet of carpeting. What dimensions should the rug have? The dimensions of the rug should be blank ft.
Found 2 solutions by ikleyn, jorel1380:
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1066615.html

Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
The room is 18 x 31 feet, yielding an area of 558 sq.ft. Let w be the width of the strip of bare floor around the carpet. Then:
(31-2w)(18-2w)=300
558-98w+4w�=300
4w�-98w+258=0
2w�-49w+129=0
(2w-43)(w-3)=0
w=43/2 or 3
Picking the most logical choice, we choose 3 ft. as the width of the strip, giving us a rug of 31-6 x 18-6, or 25' x 12' ft (300 sq.ft.). ☺☺☺☺
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