Answer :
The width of rectangle is [tex]6x^2[/tex]
Solution:
Given that,
[tex]\text{Length of rectangle } = 4x^2+12x[/tex]
[tex]\text{Area of rectangle } = 24x^4+72x^3[/tex]
To find: width of rectangle
The area of rectangle is given by formula:
[tex]\text{Area of rectangle } = length \times width[/tex]
Therefore, width is given as:
[tex]width = \frac{\text{Area of rectangle}}{length}[/tex]
Substituting the given values we get,
[tex]width = \frac{24x^4+72x^3}{4x^2+12x}[/tex]
Factor out 24 and [tex]x^3[/tex] from numerator
[tex]width = \frac{24x^3(x+3)}{4x^2+12x}[/tex]
Factor out 4 and x from denominator
[tex]width = \frac{24x^3(x+3)}{4x(x+3)}[/tex]
Cancel the common terms in numerator and denominator
[tex]width = 6x^2[/tex]
Thus the width of rectangle is [tex]6x^2[/tex]