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?

l = (7x² + 3) m; w = 2x² m

Step-by-step explanation:

(1) Monomial factors

Factors of 6: 1, 2, 3, 6

Factors of 14: 1, 2, 7, 14

The highest common factor of 6 and 14 is 2.

Factors of x²: x, x²

Factors of x⁴: x, x², x³, x⁴

The highest common factor of x² and x⁴ is x².

The highest common factor of 6x² and 14x⁴ is 2x².

(2) Solve for length and width

dа ta:

(1) A = 14x⁴ + 6x²

(2) w = 2x²

Calculations:

A = lw Divide each side by w

(3) l = A/w Insert (1) and (2) into (3)

l = (14x⁴ + 6x²) / (2x²) Divide both sides by (2)

l = (7x² + 3)