Answer:
The Width of the Rectangle =[tex]10y^6[/tex]
[tex]\text{Length of the Rectangle}=210y^8[/tex]
Step-by-step explanation:
The area of the rectangle [tex]=70y^8 30y^6.[/tex]
We are told that the width of the rectangle is equal to the greatest common monomial factor of [tex]70y^8 \: and\: 30y^6.[/tex]
Let us determine the greatest common monomial factor of [tex]70y^8 \: and\: 30y^6.[/tex]
Express each term as a product to pick out the common factors:
[tex]70y^8 =7X10Xy^6Xy^2\\30y^6=3X10Xy^6[/tex]
In the two terms, the common terms are 10 and [tex]y^6[/tex]. Therefore their greatest monomial factor =[tex]10y^6[/tex]
The Width of the Rectangle =[tex]10y^6[/tex]
Recall: Area of a Rectangle =Length X Width
[tex]70y^8 30y^6=Length X 10y^6\\Length =70y^8 30y^6 \div 10y^6 \\=\dfrac{70X30Xy^8Xy^6}{10y^6} =210y^8\\\text{Length of the Rectangle}=210y^8[/tex]
