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

Answer:

The length and width of the parking lot are $\frac{46}{3}$ meters and $\frac{23}{2}$ meters, respectively.

Step-by-step 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:

$A = \left(x-\frac{7}{2}\,m \right)\cdot \left(x+\frac{1}{3}\,m \right)$

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

$w =\left(15\,m-\frac{7}{2}\,m \right)$

$w = \frac{23}{2}\,m$

$l =\left(15\,m+\frac{1}{3}\,m \right)$

$l = \frac{46}{3}\,m$

The length and width of the parking lot are $\frac{46}{3}$ meters and $\frac{23}{2}$ meters, respectively.