The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the length of the floor and whose width is 2 feet less than the width of the floor. If the area of the carpet is 160 square feet, what is the length, in feet, of the floor?\

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

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