Answer:
Width: [tex]2x^{2}[/tex]
Lenght: [tex](7x^{2}+3)[/tex]
Step-by-step explanation:
1. The prime factorization of the monomial is:
[tex]14x^{4}=2*7*x*x*x*x\\6x^{2}=2*3*x*x[/tex]
2. The product of the common factors is:
[tex]2*x*x=2x^{2}[/tex]
3. The greatest common monomial factor is: [tex]2x^{2}[/tex]
4. The formula for calculate the area of a rectangle is:
[tex]A=L*W[/tex]
Where L is the length and W is the width
5. Therefore, if the greatest common monomial factor monomial of the area of [tex]14x^{4}+6x^{2}[/tex] is [tex]2x^{2}[/tex] and the area is the product of the lenght and the width, you have that the lenght is:
[tex]2x^{2}(7x^{2}+3)[/tex]
Length:
[tex](7x^{2}+3)[/tex]
