Algebra

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How to find dimensions of a field when given length of fencing and area?
Hi I really appreciate your help on this.
The question states that I have a field of area 650 square metres and fencing of 110 metres. I must give 3 possible sets of dimensions of the field and the fencing need not cover all four sides of the field.

Oh I forgot to mention that quadratic algebra and graphing utility must be used.
Thank you so much.

  • Algebra -

    A = Area

    F = Fencing

    W = Width

    L = Length



    A = W * L = 650 m ^ 2

    W * L = 650 Divide both sides by L

    W = 650 / L



    F = 2 W + 2 L = 2 ( W + L ) = 110 m

    2 ( W + L ) = 110 Divide both sides by 2

    W + L = 110 / 2

    W + L = 55

    650 / L + L = 55 Multiply both sides by L

    650 + L * L = 55 L

    650 + L ^ 2 = 55 L

    L ^ 2 - 55 L + 650 = 0

    The exact solutions are :

    L = ( 5 / 2 ) * [ 11 + sqrt ( 17 ) ]

    approx. 37.81 m


    and

    L = ( - 5 / 2 ) * [ - 11 + sqrt ( 17 ) ]

    approx. 17.19 m


    When L = 37.81 m

    W = 650 / 37.81 = 17.19 m


    When L = 17.19 m

    W = 650 / 17.19 = 37.81 m

    Dimensions of a field:

    37.81 m X 17.19 m



    If you don't know how solve equation L ^ 2 - 55 L + 650 = 0

    in google type:

    quadratic equation online

    When you see list of results click on:

    Free Online Quadratic Equation Solver:Solve by Quadratic Formula

    When page be open in rectangle type:

    L ^ 2 - 55 L + 650 = 0

    and click option: solve it!

    You wil see solution step-by-step

  • Algebra -

    If you must draw function :

    L ^ 2 - 55 L + 650 = 0


    In google type:
    functions graphs online

    When you see list of results click on:

    rechneronline.de/function-graphs/


    When page be open in blue rectangle type:

    x ^ 2 - 55 x + 650 = 0

    Set:

    Range x-axis from - 20 to 80

    Range y-axis from - 200 to 800

    And click option: Draw

  • Algebra -

    CORRECTION :


    When page be open in blue rectangle type:

    x ^ 2 - 55 x + 650

    Set:

    Range x-axis from - 20 to 80

    Range y-axis from - 200 to 800

    And click option: Draw

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