The rectangle below has an area of 6n^4+20n^3+14n^26n 4 +20n 3 +14n 2 6, n, start superscript, 4, end superscript, plus, 20, n, cubed, plus, 14, n, squared. The width of the rectangle is equal to the greatest common monomial factor of 6n^4, 20n^3,6n 4 ,20n 3 ,6, n, start superscript, 4, end superscript, comma, 20, n, cubed, comma and 14n^214n 2 14, n, squared. What is the length and width of the rectangle?

Given:

Area of rectangle =

Width of the rectangle is equal to the greatest common monomial factor of .

To find:

Length and width of the rectangle.

Solution:

Width of the rectangle is equal to the greatest common monomial factor of is

Now,

So, width of the rectangle is .

Area of rectangle is

Taking out GCF, we get

We know that, area of a rectangle is the product of its length and width.

Since, width of the rectangle is , therefore length of the rectangle is .