Question 1123166
 Cynthia Besch wants to buy a rug for a room that is 26 ft wide and 34 ft long.
 She wants to leave a uniform strip of floor around the rug.
 She can afford to buy 384 square feet of carpeting.
 What dimensions should the rug​ have? 
:
let x = the width of the uniform strip around the rug
then the dimensions of the rug will be (34-2x) by (26-2x)
The equation
(34-2x) * (26-2x) = 384 sq/ft
FOIL
884 - 68x - 52x + 4x^2 = 384
Arrange as a quadratic equation
4x^2 - 120x + 884 - 384 = 0
4x^2 - 120x + 500 = 0
simplify, divide by 4
x^2 - 30x + 125 = 0
Factors easily to
(x-25)(x-5) = 0
only 1 solution makes sense
x = 5 ft is the width of the uniform strip around the rug
Find the dimensions of the rug
34 - 2(5) = 24 ft
26 - 2(5) = 16 ft
the rug should be 24 by 16 which has an area: 24*16 = 384