The period (the time for one complete oscillation) of a pendulum is directly proportional to the square root of the length of the pendulum, and a pendulum of length 8 ft has a period of 2 seconds. Find a mathematical model expressing the period of a pendulum as a function of its length:

Why is the answer equal to $\displaystyle P(x) = \sqrt {\frac{x}{2}}$?

and thanks