Answer:
[tex]Width = 3y^{2} \\Length = 4 + 7y^{3}[/tex]
Step-by-step explanation:
The greatest monomial factor of [tex]12y^{2}[/tex] and [tex]21y^{5}[/tex] is equal to the product of the greatest common factor of the coefficients and the greatest common factor of the variables. And so, since the greatest common factor of the coefficients is 3 and the greatest common factor of the variables is [tex]y^{2}[/tex], then the greatest monomial factor is [tex]3y^{2}[/tex].
Now that we know the width (since in this case it is said that the greatest monomial factor is equal to the width). We can easily find out the length since we knot that the area of a rectangle is equal to length times width, therefore we can get length by dividing the area by the width. And so we get that the length is equal to...
[tex]Length = \frac{12y^{2} + 21y^{5} }{3y^{2} }[/tex]
[tex]Length = 4 + 7y^{3}[/tex]
So now we know that...
[tex]Width = 3y^{2} \\Length = 4 + 7y^{3}[/tex]
