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The parallelogram shown has

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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The parallelogram shown has

Post Thu May 19, 2016 3:43 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])


    The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

    A) 1/2

    B) 1/root2

    C) 1/2root2

    D) 1/root3

    E) 1/2root3

    OA: D

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    OptimusPrep Master | Next Rank: 500 Posts
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    Post Thu May 19, 2016 7:56 pm
    boomgoesthegmat wrote:


    The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

    A) 1/2

    B) 1/root2

    C) 1/2root2

    D) 1/root3

    E) 1/2root3

    OA: D
    Assume the length of each side = x

    The other angles would be 60, 120 and 120.
    Diagonal divides the parallelogram into half

    Hence the shorter diagonal will make two equilateral triangles
    Length of the shorter diagonal = length of side = x

    For the longer diagonal.
    The diagonal will divide the parallelogram in to isosceles triangles with angles 30, 120, 30
    Dropping a perpendicular from top most point on to the diagonal, we have two triangles with angles 30, 60 and 90 with base as half the length of diagonal

    Hypotenuse = x,
    Cos 30 = base/x
    base = (√3/2)*x

    Hence the length of the diagonal = √3x

    Ratio of the shorter to the longer diagonal = x : √3x = 1: √3

    Correct Option: D

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