Math - Algebra

Ti'a rectangular gaden has perimeter of 20 meters. She wants its area to be at least 24 square metesr. Find the interval for the possible length of Tia's garden.

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asked by James
  1. if the garden is x by y meters,
    x+y = 10
    and xy >= 24
    so,

    x(10-x) >= 24
    x^2 - 10x + 24 <= 0
    (x-4)(x-6) <= 0
    since the parabola open up, the graph is below the x-axis between the roots.

    the roots are at x=4 and x=6
    So, we need x <= 4 <= 6
    Since usually the length is greater than the width, that means we should choose

    √24 <= x <= 6

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    posted by Steve

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