Packing squares in a square.

Geometry Level 3

Units squares are packed in another square as shown in the figure.

This unique packing arrangement was discovered by Frits Goebel from the University of Amsterdam in 1979.

If the area of the green portion can be expressed as

(A*sqrt(B) + 1)/B - B, where A and B are integers,

Then find A + B


The answer is 12.

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