Question

The area of a rectangular parking lot is represented by A = 6x^2 − 19x − 7 If x represents 15 m, what are the length and width of the parking lot?

Answer 1

The length and width of the parking lot are
`(46)/(3)` meters and
`(23)/(2)` meters, respectively.

Explanation:

The surface formula (
`A`) for the rectangular parking lot is represented by:

`A = w\cdot l`

Where:

`w` - Width of the rectangle, measured in meters.

`l` - Length of the rectangle, measured in meters.

Since, surface formula is a second-order polynomial, in which each binomial is associated with width and length. If
`A = 6\cdot x^(2)-19\cdot x -7`, the factorized form is:

`A = \left(x-(7)/(2)\,m \right)\cdot \left(x+(1)/(3)\,m \right)`

Now, let consider that
`w = \left(x-(7)/(2)\,m \right)` and
`l = \left(x+(1)/(3)\,m \right)`, if
`x = 15\,m`, the length and width of the parking lot are, respectively:

`w =\left(15\,m-(7)/(2)\,m \right)`

`w = (23)/(2)\,m`

`l =\left(15\,m+(1)/(3)\,m \right)`

`l = (46)/(3)\,m`

The length and width of the parking lot are
`(46)/(3)` meters and
`(23)/(2)` meters, respectively.