Answer:
1 feet wide
Step-by-step explanation:
Let the even strip around 4 sides of the rug be "x" ft.
So, we can say:
The rug's length is 15 - x - x [from both side] = 15 - 2x
The rug's width is 20 - x - x = 20 - 2x
Rug (being a rectangle) will have an area:
Area = length * width
234 = (20 - 2x) (15 - 2x)
Multiplying and solving this equation we will get x:
[tex]234 = (20 - 2x) (15 - 2x)\\234=300-40x-30x+4x^2\\4x^2-70x+66=0[/tex]
Solving we get:
x = 16.5
x = 1
Since, x = 16.5 is not a feasible solution (you cant take out 16.5 from each side because one side is 15 total and another side is 20 total), x = 1 is the solution.
So,
She will have a strip that is 1 feet wide
