Cynthia besch wants to buy a rug for a room that is 18 ft wide and 30 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 220 square feet of carpeting. what dimensions should the rugâ have?
Since the strip around the outside of the rug will be uniform, the dimensions of the rug will have the form (18 - x) in width and (30 - x) in length, where x is equal to twice width of the strip.
We can use this data to set up an equation.
(18 - x) (30 - x) = 220
x^2 - 48 x + 540 = 220
x^2 - 48 x + 320 = 0
(x - 8) (x - 40) = 0
x = 8 or x = 40
Since x = 40 is too wide for the strip, the correct solution is x = 8
The width of the rug is: 18 - x = 10 feet
The length of the rug is: 30 - x = 22 feet
The dimensions of the rug are 10 feet x 22 feet.
Note that the area is equal to 220 square feet.
