Answer:
20ft
Step-by-step explanation:
We have two unknowns, the length and the width of the floor. Let us represent this by l and w respectively.
Firstly, we are told that the length of the floor is twice its width. This mathematically means that l = 2w
The width of the rectangular carpet is 2ft less than the width of the floor but the floor length is equal. This means that the width of the floor is (w - 2)ft
Now we are told that the area of the rectangular carpet is 160 sq.ft
This means the length of the carpet multiplied by the width is 160
Mathematically:
l * (w-2) = 160
We know that l = 2w, if we substitute this:
2w(w - 2) = 160
w(w -2) = 80
w^2 -2w = 80
w^2 - 2w - 80 = 0
w^2 -10w + 8w -80 = 0
w(w -10) + 8(w - 10) = 0
(w + 8)(w -10) = 0
w = -8 or 10
Since distance cannot be negative, we ignore the -8 and use the 10 only
Hence the width is 10ft
The length is 2 times the width. The length is thus 2 * 10ft = 20ft
