Investigating Adidas

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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