Respuesta :
Answer:
The width of the rectangle is [tex]2n^2[/tex].
The length of the rectangle is [tex]3n^2+10n+7[/tex].
Step-by-step explanation:
Consider the provided information.
The area of rectangle is [tex]6n^4 + 20n^3 + 14n^2[/tex]
It is given that the width of the rectangle is the greatest common factor of [tex]6n^4, 20n^3\ and\ 14n^2[/tex].
First find the greatest common factor of [tex]6n^4, 20n^3\ and\ 14n[/tex]:
[tex]6n^4=2\times3\times n\times n\times n\times n[/tex]
[tex]20n^3=2\times2\times 5\times n\times n\times n[/tex]
[tex]14n^2=2\times7\times n\times n[/tex]
The greatest common factor is: [tex]2n^2[/tex]
Therefore, the width of the rectangle is [tex]2n^2[/tex].
Area of rectangle is: A=LW
Substitute the value of A and W in above formula.
[tex]6n^4 + 20n^3 + 14n=2n^2L\\\\L=\frac{6n^4 + 20n^3 + 14n}{2n^2}\\\\L=3n^2+10n+7[/tex]
Hence, the length of the rectangle is [tex]3n^2+10n+7[/tex]
