# Pitching a Tent

Geometry Level 5

In $$\Delta ABC$$, $$AB=17$$, $$BC=25$$, and $$AC=26$$. Square $$JKLM$$ is such that $$\overline{JK}$$ lies on $$\overline{AB}$$, $$L$$ lies on $$\overline{BC}$$, and $$M$$ lies on $$\overline{AC}$$. The length of one side of $$JKLM$$ can be written as $$\frac{m}{n}$$, where $$m$$ and $$n$$ are positive, coprime integers. Find $$m+n$$.

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