Geometry

Henry has a patio next to his house that is 15ft by 10ft. He wants to put a uniform flower bed around three sides of the patio. The area of the flower bed is 100 ft^2. What is the width of the flower bed?

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  1. Is it 6.67 ft

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  2. let the width of the uniform border be x ft
    new width = 10+2x
    new length = 15 + 2x

    area of whole thing = (10+2x)(15+2x)
    (10+2x)(15+2x) - 150 = 100
    150 + 50x + 4x^2 - 15 - 100 = 0
    4x^2 + 50x - 100 = 0
    2x^2 + 25x - 50 = 0

    doesn't factor, so use the formula
    x = (-25 ± √1025)/4
    = 1.754 or some negative

    So 1.754 ft must be added to the width and length, so the width of the flower bed must be 1.754 ft

    check:
    area of patio = 150 ft^2
    area of whole thing
    = (10+2(1.754)) (15+2(1.754))
    = 249.999.. or 250

    increase = 250 - 150 = 100
    my answer is correct

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    posted by Reiny

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