Question

Sam has a rectangular rug with an area of 48 square feet. The rug is 8 feet longer than it is wide. What is the width of the rug?

Answer 1

Given:

Arear of rectangular rug = 48 sq. feet.

The rug is 8 feet longer than it is wide.

To find:

The width of the rug.

Solution:

Let x feet be the width of the rug.

The rug is 8 feet longer than it is wide.

Length of the rug = (x+8) feet

Area of a rectangle is

`Area=Length* Width`

Arear of rectangular rug is 48 sq. feet.

`48=(x+8)* x`

`48=x^2+8x`

`0=x^2+8x-48`

Splitting the middle term, we get

`x^2+12x-4x-48=0`

`x(x+12)-4(x+12)=0`

`(x+12)(x-4)=0`

Using zero product property, we get

`(x+12)=0\text{ and }(x-4)=0`

`x=-12\text{ and }x=4`

Width cannot be negative. So,
`x=4`.

Therefore, the width of the rug is 4 feet.