Triangle + Square = Problem!

Geometry Level 4

A triangle has sides 10, 17 and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle.

The length of the side of the square is in the form \( \frac {a}{b} \), where \(a\) and \(b\) are co-prime integers. Find \(a+b\).

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