Posted by **Chris** on Friday, March 5, 2010 at 3:44pm.

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 -
**Reiny**, Friday, March 5, 2010 at 5:18pm
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 -
**Chris**, Friday, March 5, 2010 at 5:41pm
So one side of the rhombus is equal to seven? I'm still confused as to how you got your answer...

- Math -
**Reiny**, Friday, March 5, 2010 at 6:37pm
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 -
**Chris**, Saturday, March 6, 2010 at 1:33am
I see it now,because a diagonal divides a parallelogram into two congruent triangles! Thank you!!

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