Laws of Motion: JEE Main 2021 Physics question

When a body slides down from rest along a smooth inclined plane making an angle of 30$^\circ$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $\alpha$T, where $\alpha$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is ${1 \over {\sqrt x }}\left( {{{{\alpha ^2} - 1} \over {{\alpha ^2}}}} \right)$ where x = __________.