Question

Matt's den is 10 feet longer than it is wide. If the dents area is 231 square feet, what are the dimensions of the room?

The dimensions of the room are
ft.
(Use a comma to separate answers as needed.)

Answer 1

`21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}`

Explanation:

(Assuming the den is a rectangle)

Let
`x` be the length of the den. Because the length is 10 feet longer than the width, the width of the den can be represented as
`x-10`.

The area of a rectangle is given as
`l\cdot w`, therefore we can form the following equation:

`x(x-10)=231`

Expanding this, we have:

`x^2-10x=231, \\\\x^2-10x-231=0`

This factors into
`(x-21)(x+11)=0`, therefore
`x=21, \: -11`.

Because -11 is extraneous, the length of the den is
`21` feet and the width is
`21-10=11`. Thus, the dimensions of the den are
`\fbox{$21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}$}`.