Here is the rhombus ABCD, with diagonal AC equal to the sides,
we let each side and the diagonal have length s: 
 

The rhombus therefore consiste of two equilateral
triangles with a common side AC. 

So we draw the other diagonal DB, intersecting
the first diagonal at point E. Since the
diagonals of any parallogram bisect each other,
and since a rhombus is a parallelogram, the top
and bottom halves of diagonal DB are half of 60,
So DE = EB = 30.  Also AE = EC = : 

 

Since the diagonals of a rhombus are also perpendicular,
triangle AED is a right triangle, so we can use the
Pythagorean theorem.  (We could use any one of the
four right triangles since all four are congruent.)



or each side s is about 34.64101615.

Edwin