Answer:
The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.
Step-by-step explanation:
The surface formula ([tex]A[/tex]) for the rectangular parking lot is represented by:
[tex]A = w\cdot l[/tex]
Where:
[tex]w[/tex] - Width of the rectangle, measured in meters.
[tex]l[/tex] - 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 [tex]A = 6\cdot x^{2}-19\cdot x -7[/tex], the factorized form is:
[tex]A = \left(x-\frac{7}{2}\,m \right)\cdot \left(x+\frac{1}{3}\,m \right)[/tex]
Now, let consider that [tex]w = \left(x-\frac{7}{2}\,m \right)[/tex] and [tex]l = \left(x+\frac{1}{3}\,m \right)[/tex], if [tex]x = 15\,m[/tex], the length and width of the parking lot are, respectively:
[tex]w =\left(15\,m-\frac{7}{2}\,m \right)[/tex]
[tex]w = \frac{23}{2}\,m[/tex]
[tex]l =\left(15\,m+\frac{1}{3}\,m \right)[/tex]
[tex]l = \frac{46}{3}\,m[/tex]
The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.
