Question

The rectangle below has an area of 14x^4 + 6x^2 square meters. The width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x^4 and 6x^2. What is the length and width of the rectangle?

Answer 1

Width:
`2x^(2)`

Lenght:
`(7x^(2)+3)`

Explanation:

1. The prime factorization of the monomial is:

`14x^(4)=2*7*x*x*x*x\\6x^(2)=2*3*x*x`

2. The product of the common factors is:

`2*x*x=2x^(2)`

3. The greatest common monomial factor is:
`2x^(2)`

4. The formula for calculate the area of a rectangle is:

`A=L*W`

Where L is the length and W is the width

5. Therefore, if the greatest common monomial factor monomial of the area of
`14x^(4)+6x^(2)` is
`2x^(2)` and the area is the product of the lenght and the width, you have that the lenght is:

`2x^(2)(7x^(2)+3)`

Length:

`(7x^(2)+3)`