Answer:
Width [tex]10y^6[/tex] units
Length [tex]7y^2+3[/tex] units
Step-by-step explanation:
The rectangle has an area of [tex]70y^8+30y^6.[/tex]
The width of the rectangle is equal to the greatest common monomial factor of [tex]70y^8[/tex] and [tex]30y^6.[/tex] Find this monomial factor:
[tex]70y^8=2\cdot 5\cdot 7\cdot y^8\\ \\30y^6=2\cdot 3\cdot 5\cdot y^6\\ \\GCF(70y^8,30y^6)=2\cdot 5\cdot y^6=10y^6[/tex]
Hence, the width of the rectangle is [tex]10y^6[/tex] units.
The area of the rectangle can be rewritten as
[tex]10y^6(7y^2+3).[/tex]
The area of the rectangle is the product of its width by its length, then the length of the rectangle is [tex]7y^2+3[/tex] units.
