Dan wants to create the Adidas logo by cutting three strips of same sized rectangles with the width 6, labelled \(ABCD, EFGH, KLMN\) respectively. Then, he cuts the strips diagonally, at \(QR\), such that \(\cos\angle BQR=0.5\). This process continues at the other two rectangles, at \(ST\) and \(UV\) respectively, by satisfying \(\cos\angle FST = \cos\angle LUV=0.5\). If the ratio of the area of the trapeziums is \([ABQR]:[EFST]:[KLUV]=65:34:13\), and the sum of the areas is 336, then find \(\lfloor BQ+FS+LU\rfloor\) if \(BQ>AR, FS>ET, LU>KV\).
Details and Assumptions
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