Question

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?

Answer 1

The required length is 20 feet.

Explanation:

Let the length be = L

Let the width be = W

The length of a rectangular floor is twice its width.

This becomes:
`L=2W`

The length of the carpet is L

As given the carpet width is 2 feet less than the room, so
`W=W-2`

Area of the carpet is given as = 160 square feet

So, Area becomes:

`L(W-2)=160`

As L=2W, we get;

`2W(W-2)=160`

=>
`2W^(2) -4W-160=0`

Taking out 2 common, we get;

`W^(2) -2W-80=0`

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 =
`2*10=20` feet

So, the required length is 20 feet.