Answer:
Width = 2x² , Length = 7x² + 3
Step-by-step 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 = [tex]\frac{14x^{4}+6x^2 }{2x^2} =\frac{2x^2*(7x^2+3)}{2x^2} =7x^2+3[/tex]
