Answer:
The width is [tex]6x^2[/tex]
Step-by-step explanation:
The area of a rectangle is given as : [tex]Area=l\times w[/tex]
This implies that: [tex]w=\frac{Area}{l}[/tex]
We have that the length is [tex]l=4x^2+12x[/tex] and the area is [tex]Area=24x^4+72x^3[/tex]
We substitute to get:
[tex]w=\frac{24x^4+72x^3}{4x^2+12x}[/tex]
[tex]\implies w=\frac{24x^2(x^2+3x)}{4(x^2+3x)}[/tex]
We cancel out the common factors to get:
[tex]w=6x^2[/tex]
