Wednesday

January 28, 2015

January 28, 2015

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

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 8:28amlength 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

**Answer this Question**

**Related Questions**

Math - The circular rug is placed on a square floor. The rug touches all four ...

johnson - The length of a rectangular floor is 2 feet more than its width. The ...

12th grade - The length of a rectangular floor is 2 feet more than its width. ...

12th grade - The length of a rectangular floor is 2 feet more than its width. ...

12th grade - The legnth of a rectangular floor is 2 feet more than it's width. ...

Geometry - A floor measures 19' by 16'. There is a rug centered on the floor ...

math - decorator has 92 one foot square tiles to be laid around edge of 12 x 15 ...

Algebra 2 - Abey Numkena is an interior designer. She has been asked to locate ...

Precalculus - Abey Numkena is an interior designer. She has been asked to locate...

maths - A rug covers 1/4 of the floor. The area of the rug 10ft . What is the ...