Solve the following problem with the corresponding procedure and explanation:

A 25 foot long ladder is leaning against a wall, its base is sliding down the wall at the rate of 2 feet per second.

a. At what rate is the top of the ladder sliding down the wall when the base is 7, 15 and 24 feet from the wall?

b. Determine the rate at which the area of the triangle formed changes when the base is 7 feet from the wall.