# Math

posted by on .

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!!