Algebraic model for the changing area of a right triangle

A ladder length 13 m rests against a wall in such a way that its top is 5m above the ground and its bottom is 12 m from the wall. It then starts at t=0 to slide down against the wall so that after 5 seconds it reaches flat position on the floor. Assume uniform acceleration and model the base b and the altitude h of the right triangle formed by the ladder, the wall and the floor. Next, display the base-function, altitude function, Area-of-the-triangle-function as well as the rate-of-area-change-with-time-function on the same set of axes.