Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 312 square feet of carpeting. What dimensions should the rug​ have?

Answer 1

If the uniform strip has width w, then we have
(18-2w)(32-2w) = 312
You can solve for w, or just note that the above gives you
(9-w)(16-w) = 78
Now, which two factors of 78 differ by 7?

Answer 2

(18 - 2x)(32 - 2x) = 312

4x^2 - 100 x + 576 = 312 ... solve for x ... the width of the strip of floor

the rug dimensions are the room dimensions minus the strip (on both sides)