Answer:
Width = 2x²
Length = 7x² + 3
Step-by-step explanation:
∵ The area of a rectangle is [tex]14x^{4}+6x^{2}[/tex]
∵ Its width is the greatest common monomial factor of [tex]14x^{4}[/tex] and 6x²
- Let us find the greatest common factor of 14 , 6 and [tex]x^{4}[/tex] , x²
∵ The factors of 14 are 1, 2, 7, 14
∵ The factors of 6 are 1, 2, 3, 6
∵ The common factors of 14 and 6 are 1, 2
∵ The greatest one is 2
∴ The greatest common factor of 14 and 6 is 2
- The greatest common factor of monomials is the variable with
the smallest power
∴ The greatest common factor of [tex]x^{4}[/tex] and x² is x²
∴ The greatest common monomial factor of [tex]14x^{4}[/tex] and 6x² is 2x²
∴ The width of the rectangle is 2x²
To find the length divide the area by the width
∵ The area = [tex]14x^{4}+6x^{2}[/tex]
∵ The width = 2x²
∴ The length = ( [tex]14x^{4}+6x^{2}[/tex]) ÷ (2x²)
∵ [tex]14x^{4}[/tex] ÷ 2x² = 7x²
∵ 6x² ÷ 2x² = 3
∴ ( [tex]14x^{4}+6x^{2}[/tex]) ÷ (2x²) = 7x² + 3
∴ The length of the rectangle is 7x² + 3
