Question 1096124
 A rectangular rug has a decorative interior with a 1/2 foot border of uniform width around the outside.
 The length of the decorative area is 3 feet more than the width.
 If the area of the rug (including the border) is 108 ft2, find the dimensions of the rug (including the border).
:
let L = the length of the decorated area
let w = the width
Also "length of the decorative area is 3 feet more than the width"
L = w+3
:
Twice the width of the border (1 ft), is added to the decorated dimensions, therefore
(L+1)(w+1) = 108
Replace L with (w+3)
((w+3)+1)(w+1) = 108
(w+4)(w+1) = 108
FOIL
w^2 + w + 4w + 4 = 108
w^2 + 5w + 4 - 108 = 0
w^2 + 5w - 104 = 0
You can use the quadratic formula, a=1, b=5, c=-104;but this will factor
(x+13)(x-8) = 
the positive solution is all we want here
x = 8ft is the width of the decorated area
then, obviously 11 ft is the length
Find the overall dimensions, add 1 ft
12 ft by 9 ft is the overall dimensions of the rug
:
;
Check by finding the area with these dimensions: 12 * 9 = 108