2015 AIME II Problem 7

Triangle ABC has side lengths AB = 12, BC = 25, and CA = 17. Rectangle PQRS has vertex P on \overline{AB}, vertex Q on \overline{AC}, and vertices R and S on \overline{BC}. In terms of the side length PQ = w, the area of PQRS can be expressed as the quadratic polynomial

\text{Area}(PQRS) = \alpha w - \beta \cdot w^2.

Then the coefficient \beta = \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.

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.