Posted by **Sejul** on Monday, October 10, 2011 at 7:17am.

length of rectantular rug is 7/6 its width.

rug is placed on floor with 1 foot margin all around.

area of floor is 4 times that of margin.

find the dimensions of the room.

- algebra -
**Reiny**, Monday, October 10, 2011 at 8:28am
length of rug = 7x

width of rug = 6x , (that avoids fractions)

floor is (7x+2) by (6x+2)

area of margin = (7x+2)(6x+2) - 42x^2

floor is 4 times the margin

(7x+2)(6x+2) = 4[(7x+2)(6x+2) - 42x^2 ]

42x^2 + 26x + 4 = 4[42x^2 + 26x + 4 - 42x^2]

42x^2 - 78x - 12 = 0

7x^2 - 13x - 2 = 0

(x-2)(7x+1) = 0

x = 2 or a negative

so the floor is

7x+2 by 6x+2 or

16 by 14 or 224 ft^2

and the rug is (7x)(6x) = 168 ft^2

margin = 224-168 = 56

is 4(56) = 224 ??, YES

The room is 16 ft by 14 ft

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