Question

The rectangle below has an area of 14x^4+6x^214x 4 +6x 2 square meters. The width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x^414x 4 and 6x^26x 2 . What is the length and width of the rectangle?

Answer 1

Width = 2x² , Length = 7x² + 3

Explanation:

The area of the rectangle = 14x⁴ + 6x²

The width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x⁴ and 6x²

Factors of 14: 1 * 2 * 7

Factors of 6: 1 * 2 * *3

∴ The greatest common monomial factor of 14 and 6 = 2

Factors of x⁴: x , x² , x³ , x⁴

Factors of x²: x , x²

∴ The greatest common factor of x⁴ and x² = x²

∴ Width = 2x²

∵ Area = length times the width

∴ Length = Area/Width

Length =
`(14x^(4)+6x^2 )/(2x^2) =(2x^2*(7x^2+3))/(2x^2) =7x^2+3`