Answer:
[tex]3(3x+2)=9x+6[/tex] units.
Step-by-step explanation:
We have been given that a rectangle has an area of [tex]45x^2-42x-48[/tex] and a width of [tex]5x-8[/tex]. We are asked to find the length of the rectangle.
Since we know that area of a rectangle equals to the product of its width and length, so to find the length of our given rectangle we will divide area of the rectangle by its width.
[tex]\text{Length of rectangle}=\frac{45x^2-42x-48}{5x-8}[/tex]
[tex]\text{Length of rectangle}=\frac{3(15x^2-14x-16)}{5x-8}[/tex]
[tex]\text{Length of rectangle}=\frac{3(15x^2+10x-24x-16)}{5x-8}[/tex]
[tex]\text{Length of rectangle}=\frac{3(5x(3x+2)-8(3x+2))}{5x-8}[/tex]
[tex]\text{Length of rectangle}=\frac{3((3x+2)(5x-8))}{5x-8}[/tex]
Upon cancelling [tex]5x-8[/tex] from numerator and denominator we will get,
[tex]\text{Length of rectangle}=3(3x+2)[/tex]
[tex]\text{Length of rectangle}=9x+6[/tex]
Therefore, the length of the rectangle is [tex]3(3x+2)=9x+6[/tex] units.
