If one of the diagonals of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio :

Let ABCD is a rhombus in which AB = BC = CD = DA = diagonal CA.
In triangle ABC ,
AB = BC = CA , therefore ∠B = 60°
∠D = ∠B = 60°
∠A=180 - ∠B = 180° - 60° =120°
∠C = ∠A=120°
Hence ,The ratio of diagonals = √2 : 1