What dimensions should the rug have?

Question

A person wants to buy a rug for a room that is 23 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 588 square feet of carpeting. What dimensions should the rug have?

Answer 1

let x = width of uniform strip

 

23-x = width of rug

30-x = length of rug

 

588 = area of rug

 

(23-x)(30-x) = 588

 

x² - 53x + 690 = 588

 

x² - 53x + 102 =0

 

(x-51)(x-2) = 0

 

x = 51, x=2

 

We can't use 51 because that is longer than the length or width of the room. 

 

Therefore, the uniform strip would be 2 feet. 

 

That means the rug would have to be 28 feet long x 21 feet wide.