Answer:
Width = [tex]3y^{2}[/tex]
Length = [tex]4+7y^{3}[/tex]
Step-by-step explanation:
Area of the rectangle = [tex]12y^{2}+21y^{5}[/tex]
Width of the rectangle is greatest common monomial factor of [tex]12y^{2}[/tex] and [tex]21y^{5}[/tex]. Monomial means consisting of a one term only. Terms in an algebraic expression are distinguished by symbols of addition and subtraction. So, in expression of Area there are 2 terms. Factorizing the expression of Area will give us the width and length of the rectangle as shown below:
[tex]Area = 12y^{2}+21y^{5}\\\\ Area=3y^{2}(4+7y^{3})[/tex]
Since, Area of a rectangle is the product of its length and width, and the monomial factor represents the width, we can write:
Width = [tex]3y^{2}[/tex]
Length = [tex]4+7y^{3}[/tex]
