11. A $3 \mathrm{~cm}$ wide strip is grey on one side and white on the other. Maria folds the strip, so that it fits inside a rectangle of length $27 \mathrm{~cm}$, as shown. The grey trapeziums are identical. What is the length of the original strip?
A $36 \mathrm{~cm}$
B $48 \mathrm{~cm}$
C $54 \mathrm{~cm}$
D $57 \mathrm{~cm}$
E $81 \mathrm{~cm}$
11. D Let the length of the shorter of the two parallel sides of the grey trapeziums be $x$ $\mathrm{cm}$. Since the folded shape is $27 \mathrm{~cm}$ long and the strip is $3 \mathrm{~cm}$ wide, we have $3+x+3+x+3+x+3+x+3=27$ which has solution $x=3$. Hence the length of the longer of the two parallel sides of the grey trapezium is $(3+x+3) \mathrm{cm}=9 \mathrm{~cm}$. Also, since the height of each trapezium is equal to the width of the strip, the height is $3 \mathrm{~cm}$ and hence the height of each of the small rectangles is $(6-3) \mathrm{cm}$. Therefore the total length of the strip (along the edge marked in the diagram) is
$$
(6+9+3+3+3+3+3+9+3+3+3+3+6) \mathrm{cm}=57 \mathrm{~cm} .
$$