Follow The Fold

Geometry Level 3

In rectangle ABCD (below left), AB=3AB=3 and BC=5BC=5. The corner at C is folded up (below right) and lands on AB\overline{AB} so that AC=2AC=2 and CB=1CB=1.

The area of quadrilateral CPNM can be written as mn\frac{m}{n}, where m and n are positive, coprime integers. Find m+nm+n.

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