Answer: The correct width is given by (C) 10x - 6.
Step-by-step explanation: Given that the area 'A' and the length 'l' of a rectangle r as follows:
[tex]A=120x^2+78x-90,\\\\l=12x+15.[/tex]
We are to find the width, 'w' of the rectangle.
The AREA of a rectangle is equal to the product of its length and breadth.
So, in the given rectangle, we have
[tex]A=l\times w\\\\\Rightarrow w=\dfrac{A}{l}.[/tex]
Therefore, the width is given by the quotient of the area and the length of the rectangle.
The width can be calculated as follows:
[tex]w\\\\=\dfrac{A}{l}\\\\=\dfrac{120x^2+78x-90}{12x+15}\\\\\\=\dfrac{10x(12x+15)-6(10x+15)}{12x+15}\\\\\\=\dfrac{(10x-6)(12x+15)}{(12x+15)}\\\\=10x-6.[/tex]
Therefore, width of the rectangle, w = 10x - 6.
