Math

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Abigail Adventuresome took a shortcut along the diagonal of a rectangular field and saved a distance equal to 1/3 the length of the longer side.Find the retio of the length of the shorter side of the rectangle to that of the longer side.

  • Math -

    let the longer side be x and the shorter side by y
    then the hypotenuse is √(x^2 + y^2)

    We are told
    √(x^2 + y^2) = x + x/3
    √(x^2 + y^2) = 4x/3
    square both sides
    x^2 + y^2 = 16x^2/9
    9x^2 + 9y^2 = 16x^2
    9y^2 = 7y^2
    take √ of both sides, using only the positive case
    3y = (√7)x
    y/x = √7/3
    y:x = √7 : 3

  • Math -

    that actually is wrong because i found the answer to that in the back of my book and the answer is 5/12, but i have no idea how to get to that answer

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