Question

Tonya has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it’s width

Answer 1

The length of the rug is
`7\ ft`

The width of the rug is
`3\ ft`

Explanation:

Let

x----> the length of the rug

y----> the width of the rug

we know that

The area of the rug is

`A=xy`

`A=21\ ft^(2)`

so

`21=xy` -----> equation A

`x=y+4` -----> equation B

substitute equation B in equation A and solve for y

`21=(y+4)y`

`y^(2)+4y-21=0`

Solve the quadratic equation by graphing

The solution is
`y=3\ ft`

see the attached figure

Find the value of x

`x=3+4=7\ ft`

therefore

The length of the rug is
`7\ ft`

The width of the rug is
`3\ ft`