Algebra

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To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 120 ft. of fencing material.
a. What quadratic function represents the area of the rectangular enclosure, where x is the distance from the house?

b. what dimensions will maximize the area of the enclosure?

  • Algebra -

    Let the length parallel to the house be y
    let each of the other two equal sides be x

    2x + y = 120
    y = 120 - 2x

    Area = xy
    = x(120 - 2x) or -2x^2 + 120x

    b) you want the vertex.
    x of the vertex is -120/(-4) = 30
    when x = 30
    y = 60
    Maximum area = xy = 1800 ft^2

  • Algebra -

    Roller coaster that has uphill climb of 255 feet at an angle of 38 degrees on its largest hill

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