Question

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.

Answer 1

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