Respuesta :
Answer:
Width of rectangle = [tex]2x^{2}[/tex]
length of rectangle = [tex]7x^{2} +3[/tex]
Step-by-step explanation:
Area = [tex]14x^{4}+6x^{2}[/tex]
The greatest common monomial factor is that factor that [tex]14x^{4}[/tex] and [tex]6x^{2}[/tex] will divide without leaving a remainder.
[tex]14x^{4} = 2*7*x*x*x*x\\6x^{2} = 2*3*x*x[/tex]
The common factors are 2, x and x
Therefore, greatest common factor = [tex]2*x*x=2x^{2}[/tex]
Width of rectangle = Greatest common factor = [tex]2x^{2}[/tex]
Area of a rectangle = length * breadth
[tex]length=\frac{area}{width}=\frac{14x^{4}+6x^{2} }{2x^{2} } \\\\ length = \frac{14x^{4}}{2x^{2}} +\frac{6x^{2} }{2x^{2} } \\\\length=7x^{2} +3[/tex]
Length of rectangle = [tex]7x^{2} +3[/tex]
Area of rectangle is the product of length and width.
Length is [tex]7x^{2} +3[/tex] and width is [tex]2x^{2}[/tex].
Since, Area of rectangle is given that [tex]14x^{4}+6x^{2}[/tex]
Area of rectangle = [tex]14x^{4}+6x^{2}[/tex]
Greatest Common Monomial Factor is a factor which can be take common in each term of a given polynomial.
Now, we have to find Monomial Factor of [tex]14x^{4}+6x^{2}[/tex]
We observe that, [tex]2x^{2}[/tex] is common in both term of given polynomial.
[tex]14x^{4}+6x^{2}=2x^{2} (7x^{2} +3)[/tex]
So, Common Monomial Factor is [tex]2x^{2}[/tex]
Since, width of the rectangle is equal to the greatest common monomial factor.
Thus, width of rectangle = [tex]2x^{2}[/tex]
[tex]Area = length*width\\\\length=\frac{Area}{width} \\\\length=\frac{14x^{4}+6x^{2} }{2x^{2} } =\frac{2x^{2} (7x^{2} +3)}{2x^{2} } \\\\length=7x^{2} +3[/tex]
Learn more:
https://brainly.com/question/25665489
