Five Similar Rectangles

Geometry Level 4

The four rectangles \(A\), \(B\), \(C\), and \(D\) below, as well as the big rectangle they compose, are all similar to each other. The ratio of the area of \(A\) to the area of \(B\) can be written as \(a:b\), where \(a\) and \(b\) are positive coprime integers. Give \(a+b\).

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