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). Show all work. Answer with a complete sentence.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
Answer by greenestamps(13198)  (Show Source):
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