In a ‘Quick March’, a standard marching step involves 110 steps per minute. This is the regulated pace used by military personnel while performing synchronized walking drills.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.