Question

Kevin wants to buy an area rug for his living room. He would like the area rug to be no smaller that 48 square feet and no bigger than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the width?

Answer 1

`6\leq W\leq 8`

`8\leq L\leq 10`

Explanation:

Let the length of the rug be = L

Let the width of the rug be = W

Area =
`L* W`

The length is 2 feet more than the width, so
`L=W+2`

Area =
`(W+2)* W`

=
`W^(2) +2W`

Now given is that the area of rug to be no smaller that 48 square feet and no bigger than 80 square feet.

This can be modeled as:

`48\leq W^(2) +2W\leq 80`

Solving it separately:

`48\leq W^(2) +2W`

=>
`0\leq W^(2)+2W \leq -48`

=>
`6\leq W`

`W^(2) +2W-80\leq 0`

=>
`W\leq 8`

We have the following result:

`6\leq W\leq 8`

And length will be :

`6+2\leq L\leq 8+2`

`8\leq L\leq 10`