2001 AIME I Problem 9

In triangle A B C, A B=13, B C=15 and C A=17. Point D is on \overline{A B}, E is on \overline{B C}, and F is on \overline{C A}. Let A D=p \cdot A B, B E=q \cdot B C, and C F=r \cdot C A, where p, q, and r are positive and satisfy p+q+r=2 / 3 and p^{2}+q^{2}+r^{2}=2 / 5. The ratio of the area of triangle D E F to the area of triangle A B C can be written in the form m / n, where m and n are relatively prime positive integers. Find m+n.