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

Width =
`3y^(2)`

Length =
`4+7y^(3)`

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)`