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23 May, 11:46

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?

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  1. 23 May, 14:47
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    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)
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