contestada

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?

Respuesta :

Answer:

The required length is 20 feet.

Step-by-step explanation:

Let the length be = L

Let the width be = W

The length of a rectangular floor is twice its width.

This becomes: [tex]L=2W[/tex]

The length of the carpet is L

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

Area of the carpet is given as = 160 square feet

So, Area becomes:

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

As L=2W, we get;

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

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

Taking out 2 common, we get;

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

Solving this quadratic equation, we get:

(W-10) and (W+8)

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

Now, the width = 10 feet

And Length = [tex]2\times10=20[/tex] feet

So, the required length is 20 feet.

Otras preguntas