2003 AIME II Problem 11

Triangle ABC is a right triangle with AC = 7, BC = 24, and right angle at C. Point M is the midpoint of AB, and D is on the same side of line AB as C so that AD = BD = 15. Given that the area of triangle CDM may be expressed as \frac {m\sqrt {n}}{p}, where m, n, and p are positive integers, m and p are relatively prime, and n is not divisible by the square of any prime, find m + n + p.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.