SOLUTION: A rhombus has one diagonal equal to the sides. The other diagonal has length 60. How long are the sides?

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