If the rhombus has sides of length $\displaystyle a$ and $\displaystyle \theta$ is one of its interior angles, the diagonals have lengths $\displaystyle 2a\cos{\frac{\theta}{2}}$ and $\displaystyle 2a\sin{\frac{\theta}{2}}$. The two are equal if and only if $\displaystyle \theta=\frac{\pi}{2}$.