A staircase consists of n identical steps, each with a rise of h metres and a tread of t metres. A hand-rail is to be fixed in a single straight line from the bottom of the first step to the top of the nth step.
a. (i) Show that the length L of the hand-rail is given by L=nh2+t2.
b. (ii) Using this result, find the length of the hand-rail, correct to two decimal places, for a staircase of 5 steps where h = 0.18 m and t = 0.25 m.