algebra
posted by Sejul .
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
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
(x2)(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 = 224168 = 56
is 4(56) = 224 ??, YES
The room is 16 ft by 14 ft
Respond to this Question
Similar Questions

Algebra 2
Abey Numkena is an interior designer. She has been asked to locate an oriental rug for a new corporate office. As a rule, the rug should cover 1/2 of the total floor area with a uniform width surrounding the rug. a. if the dimensions … 
12th grade
The legnth of a rectangular floor is 2 feet more than it's width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visible on all sides. What should the … 
12th grade
The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visible on all sides. What should the … 
12th grade
The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visible on all sides. What should the … 
johnson
The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visible on all sides. What should the … 
Math
The circular rug is placed on a square floor. The rug touches all four walls. How much of the floor space is not covered by the rug? 
algebra
A 4m by 6m rug covers half of the floor area of a room and leaves a uniform strip of bare floor around the edges. What are the dimensions of the room? 
math
decorator has 92 one foot square tiles to be laid around edge of 12 x 15 ft room. A rectangular rug that is 3 feet longer than it is wide is to be placed in center area where there are not tiles. Find the dimensions of the smallest … 
Precalculus
Abey Numkena is an interior designer. She has been asked to locate an oriental rug for the new corporate office. As a rule, the rug should cover 1/2 of the total floor area with a uniform width surrounding the rug. a) If the dimensions … 
Algebra 2
The area of a dining room is 160 square feet. a rectangular rug placed in the center of the room is twice as long as it is wide. If the rug is bordered by feet of hardwood floor on all sides, find the dimensions of the rug.