I need help with the dimensions of 
a strip of flooring around a rug.  

Catarina and Jose want to buy a rug 
for a room that is 15 feet by 20 feet.  
They want to leave an even strip of 
flooring uncovered around the edges 
of the room.  how wide a strip will 
they have if they buy a rug with an 
area of 234 square feet? 

 _x________________________x_
|   |                    |   |x
|___|____________________|___| 
|   |     20-2x          |   |
|   |               15-2x|   |
|   |                    |   |
|___|____________________|___|
|x  |                    |   |x
|___|____________________|___|


Area of rug = 234
Area of rug = LW = (20-2x)(15-2x)

so,

(20-2x)(15-2x) = 234

Use FOIL:

300 - 40x - 30x + 4x² = 234

      300 - 70x + 4x² = 234

      4x² - 70x + 300 = 234

       4x² - 70x + 66 = 0

Divide thru by 2

       2x² - 35x + 33 = 0

     (x - 1)(2x - 33) = 0

     x = 1, x = 16.5

The larger value is impossible, so the
only feasible answer is a 1 foot strip.

Edwin