Math

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In rhombus DEFG, if m<DEF=60, and the shorter diagonal DF has a length of 7, find the length of the side of a rhombus.

  • Math -

    In a rhombus, the diagonals right-bisect each other.
    I recognize the 30-60-90 triangle in the diagram.
    then
    x/2 = 3.5/1
    x = 7
    (sure enough, triangle DEF is equilateral)

  • Math -

    So one side of the rhombus is equal to seven? I'm still confused as to how you got your answer...

  • Math -

    Ok, I will use a different approach this time.

    Hope you make a sketch.
    Since one angle is 60º, then its opposite angle is also 60º, properties of a parallelogram.
    Which means the other angle pair is 120º each, (angle D = angle F = 120)
    Now look at your diagram, don't you see two equilateral triangles,
    triange DEF and also triangle DGF.
    So all sides in those two triangles must be equal,
    since DF = 7 , the sides of the rhomubus are 7 each.

  • Math -

    I see it now,because a diagonal divides a parallelogram into two congruent triangles! Thank you!!

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