The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths and as shown, is where m, n, and p are positive integers, m and n are relatively prime, and p is not divisible by the square of any prime. what is m + n + p?

Asales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. the representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. she uses the given expression to model the number of club members, in hundreds, after advertising for t months.