Question

The rectangle below has an area of 12y^2+21y^5 The width of the rectangle is equal to the greatest common monomial factor of 12y^2 and 21y^5 What is the length and width of the rectangle

Answer 1

Answer:

Width = $3y^{2}$

Length = $4+7y^{3}$

Step-by-step explanation:

Area of the rectangle = $12y^{2}+21y^{5}$

Width of the rectangle is greatest common monomial factor of $12y^{2}$ and $21y^{5}$. 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:

$Area = 12y^{2}+21y^{5}\\\\ Area=3y^{2}(4+7y^{3})$

Since, Area of a rectangle is the product of its length and width, and the monomial factor represents the width, we can write:

Width = $3y^{2}$

Length = $4+7y^{3}$