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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 lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor?
A. 8
B. 16
C. 20
D. 24
E. 32

Respuesta :

Answer:

Option C is correct.

Step-by-step explanation:

Let the length be L

Let the width be W

The length of a rectangular floor is twice its width.

So, we get [tex]L=2W[/tex]

The length of the carpet is L

Carpet width is 2 feet less than the room, so [tex]W=W-2[/tex]

Area of the carpet = 160 sq feet

We get :

[tex]L(W-2)=160[/tex]

As L=2W, we get

[tex]2W(W-2)=160[/tex]

=> [tex]2W^{2} -4W=160[/tex]

Equating to zero, we have

[tex]2W^{2} -4W-160=0[/tex]

Taking out 2 common

[tex]W^{2} -2W-80=0[/tex]

=> [tex]W^{2} -10W+8W-80=0[/tex]

=> [tex]W(W-10)+8(W-10)=0[/tex]

We get roots as : (W-10) and (W+8)

Hence, W = 10 and W = -8(neglect this negative value)

Now, the width = 10 feet

Length = [tex]2(10)=20[/tex] feet

Hence, option C is the answer.

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