Pre Calculas

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A GARDENER HAS 60' of edging. She wants to use it to enclose a 120 square foot rectangular area. She does not have to use up all of the edging. what are the possible lengths that a side of the rectangle can have? Answer using interval notation. Hint: if the length of the rectangle is x, and the area is 120, what is the width?

  • Pre Calculas -

    x+y <= 60
    xy = 120

    so,
    x + 120/x <= 60
    x^2 + 120 <= 60x
    x^2 - 60x + 120 <= 0
    The two roots of this equation are
    x = [60±√(3600-480)]/2 = 30±2√195

    since this is a parabola which open up, it is negative between the roots. so,

    x ∊ [30-2√195,30+2√195]

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