Pitching a Tent

Geometry Level 5

In ΔABC\Delta ABC, AB=17AB=17, BC=25BC=25, and AC=26AC=26. Square JKLMJKLM is such that JK\overline{JK} lies on AB\overline{AB}, LL lies on BC\overline{BC}, and MM lies on AC\overline{AC}. The length of one side of JKLMJKLM can be written as mn\frac{m}{n}, where mm and nn are positive, coprime integers. Find m+nm+n.

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