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Math Help - Simple Equation in One Variable ( + some Geometry)

  1. #1
    Junior Member MoniMini's Avatar
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    India
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    Post Simple Equation in One Variable ( + some Geometry)

    Hi there guys!
    I've a problem solving this Linear Equations question.

    ABCD is a rectangle with sides 36cm and 90cm. P is a point on BC, which is one of the longer sides, such that PA = 2PD.
    The length of PB is-
    a) 80cm b)18cm c)72cm d)64cm
    Alright, I drew the Rough Sketch and all... but I don't know how to proceed after that.
    I took the areas of PAD and (PAB + CDP) and the 2 sides of the equation but this way
    all the values get cancelled out and you get 1=1. I couldn't really figure out how
    Pythagorean Theorem would solve the problem either.

    Any advice will be highly appreciated

    Thanks
    ~MoniMini
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  2. #2
    Junior Member
    Joined
    Mar 2013
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    California
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    Re: Simple Equation in One Variable ( + some Geometry)

    If \quad PB = x, \quad then \quad PC = 90-x. \quad So, \quad PA = \sqrt{(36)^2 + x^2} \quad and \quad PD = \sqrt{(36)^2 + (90 - x)^2}. \quad Use \quad also \quad the \quad fact \quad PA = 2PD \quad and \quad you \quad will \quad find \quad x = PB
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