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

Answer:

Width: $2x^{2}$

Lenght: $(7x^{2}+3)$

Step-by-step 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:

$(7x^{2}+3)$