The shorter diagonal


We work with the isosceles acute triangle whose lateral sides are 12 cm long and the angle between them is 60°.

 =  =  =  = 12 cm.

As you see, the shorter diagonal has the length of 12 cm, same as the two other sides of this triangle,
so the triangle is equilateral, actually.
We could foresee it, since the isosceles triangle with one (any) angle of 60° is equiangular and equilateral.


The longer diagonal


We work with the isosceles obtuse triangle whose lateral sides are 12 cm long and the angle between them is 120°.

 =  =  =  =  =  cm.

Answer.  The diagonals of the rhombus are  12 cm  and   cm.